Decomposition of Early bird numbers - 2D graph - First 500 terms
"Early bird" numbers: write the natural numbers in a string 12345678910111213.... Sequence gives numbers which occur in the string ahead of their natural place (cf. A117804).
n |
earlybirdnum |
weight k(n) |
level L(n) |
jump |
1 |
12 |
0 |
0 |
9 |
2 |
21 |
19 |
1 |
2 |
3 |
23 |
15 |
1 |
8 |
4 |
31 |
2 |
15 |
1 |
5 |
32 |
3 |
10 |
2 |
6 |
34 |
9 |
3 |
7 |
7 |
41 |
2 |
20 |
1 |
8 |
42 |
41 |
1 |
1 |
9 |
43 |
41 |
1 |
2 |
10 |
45 |
13 |
3 |
6 |
11 |
51 |
2 |
25 |
1 |
12 |
52 |
3 |
17 |
1 |
13 |
53 |
2 |
26 |
1 |
14 |
54 |
4 |
13 |
2 |
15 |
56 |
17 |
3 |
5 |
16 |
61 |
2 |
30 |
1 |
17 |
62 |
61 |
1 |
1 |
18 |
63 |
2 |
31 |
1 |
19 |
64 |
3 |
21 |
1 |
20 |
65 |
3 |
21 |
2 |
21 |
67 |
7 |
9 |
4 |
22 |
71 |
2 |
35 |
1 |
23 |
72 |
71 |
1 |
1 |
24 |
73 |
2 |
36 |
1 |
25 |
74 |
73 |
1 |
1 |
26 |
75 |
2 |
37 |
1 |
27 |
76 |
37 |
2 |
2 |
28 |
78 |
5 |
15 |
3 |
29 |
81 |
2 |
40 |
1 |
30 |
82 |
3 |
27 |
1 |
31 |
83 |
2 |
41 |
1 |
32 |
84 |
83 |
1 |
1 |
33 |
85 |
2 |
42 |
1 |
34 |
86 |
5 |
17 |
1 |
35 |
87 |
5 |
17 |
2 |
36 |
89 |
3 |
29 |
2 |
37 |
91 |
2 |
45 |
1 |
38 |
92 |
7 |
13 |
1 |
39 |
93 |
2 |
46 |
1 |
40 |
94 |
3 |
31 |
1 |
41 |
95 |
2 |
47 |
1 |
42 |
96 |
5 |
19 |
1 |
43 |
97 |
2 |
48 |
1 |
44 |
98 |
97 |
1 |
1 |
45 |
99 |
97 |
1 |
2 |
46 |
101 |
23 |
4 |
9 |
47 |
110 |
109 |
1 |
1 |
48 |
111 |
2 |
55 |
1 |
49 |
112 |
103 |
1 |
9 |
50 |
121 |
2 |
60 |
1 |
51 |
122 |
11 |
11 |
1 |
52 |
123 |
23 |
5 |
8 |
53 |
131 |
2 |
65 |
1 |
54 |
132 |
41 |
3 |
9 |
55 |
141 |
2 |
70 |
1 |
56 |
142 |
19 |
7 |
9 |
57 |
151 |
2 |
75 |
1 |
58 |
152 |
11 |
13 |
9 |
59 |
161 |
2 |
80 |
1 |
60 |
162 |
17 |
9 |
9 |
61 |
171 |
2 |
85 |
1 |
62 |
172 |
163 |
1 |
9 |
63 |
181 |
2 |
90 |
1 |
64 |
182 |
173 |
1 |
9 |
65 |
191 |
2 |
95 |
1 |
66 |
192 |
61 |
3 |
9 |
67 |
201 |
2 |
100 |
1 |
68 |
202 |
97 |
2 |
8 |
69 |
210 |
11 |
19 |
1 |
70 |
211 |
2 |
105 |
1 |
71 |
212 |
211 |
1 |
1 |
72 |
213 |
2 |
106 |
1 |
73 |
214 |
3 |
71 |
1 |
74 |
215 |
2 |
107 |
1 |
75 |
216 |
5 |
43 |
1 |
76 |
217 |
2 |
108 |
1 |
77 |
218 |
7 |
31 |
1 |
78 |
219 |
2 |
109 |
1 |
79 |
220 |
3 |
73 |
1 |
80 |
221 |
2 |
110 |
1 |
81 |
222 |
13 |
17 |
1 |
82 |
223 |
43 |
5 |
8 |
83 |
231 |
2 |
115 |
1 |
84 |
232 |
3 |
77 |
1 |
85 |
233 |
2 |
116 |
1 |
86 |
234 |
227 |
1 |
7 |
87 |
241 |
2 |
120 |
1 |
88 |
242 |
241 |
1 |
1 |
89 |
243 |
47 |
5 |
8 |
90 |
251 |
2 |
125 |
1 |
91 |
252 |
251 |
1 |
1 |
92 |
253 |
35 |
7 |
8 |
93 |
261 |
2 |
130 |
1 |
94 |
262 |
3 |
87 |
1 |
95 |
263 |
15 |
17 |
8 |
96 |
271 |
2 |
135 |
1 |
97 |
272 |
271 |
1 |
1 |
98 |
273 |
53 |
5 |
8 |
99 |
281 |
2 |
140 |
1 |
100 |
282 |
281 |
1 |
1 |
101 |
283 |
11 |
25 |
8 |
102 |
291 |
2 |
145 |
1 |
103 |
292 |
3 |
97 |
1 |
104 |
293 |
15 |
19 |
8 |
105 |
301 |
2 |
150 |
1 |
106 |
302 |
7 |
43 |
1 |
107 |
303 |
8 |
37 |
7 |
108 |
310 |
3 |
103 |
1 |
109 |
311 |
2 |
155 |
1 |
110 |
312 |
311 |
1 |
1 |
111 |
313 |
2 |
156 |
1 |
112 |
314 |
313 |
1 |
1 |
113 |
315 |
2 |
157 |
1 |
114 |
316 |
3 |
105 |
1 |
115 |
317 |
2 |
158 |
1 |
116 |
318 |
317 |
1 |
1 |
117 |
319 |
2 |
159 |
1 |
118 |
320 |
11 |
29 |
1 |
119 |
321 |
2 |
160 |
1 |
120 |
322 |
3 |
107 |
1 |
121 |
323 |
2 |
161 |
1 |
122 |
324 |
17 |
19 |
1 |
123 |
325 |
2 |
162 |
1 |
124 |
326 |
5 |
65 |
1 |
125 |
327 |
2 |
163 |
1 |
126 |
328 |
3 |
109 |
1 |
127 |
329 |
2 |
164 |
1 |
128 |
330 |
7 |
47 |
1 |
129 |
331 |
2 |
165 |
1 |
130 |
332 |
331 |
1 |
1 |
131 |
333 |
2 |
166 |
1 |
132 |
334 |
109 |
3 |
7 |
133 |
341 |
2 |
170 |
1 |
134 |
342 |
11 |
31 |
1 |
135 |
343 |
2 |
171 |
1 |
136 |
344 |
7 |
49 |
1 |
137 |
345 |
113 |
3 |
6 |
138 |
351 |
2 |
175 |
1 |
139 |
352 |
3 |
117 |
1 |
140 |
353 |
2 |
176 |
1 |
141 |
354 |
347 |
1 |
7 |
142 |
361 |
2 |
180 |
1 |
143 |
362 |
19 |
19 |
1 |
144 |
363 |
2 |
181 |
1 |
145 |
364 |
17 |
21 |
7 |
146 |
371 |
2 |
185 |
1 |
147 |
372 |
7 |
53 |
1 |
148 |
373 |
2 |
186 |
1 |
149 |
374 |
367 |
1 |
7 |
150 |
381 |
2 |
190 |
1 |
151 |
382 |
3 |
127 |
1 |
152 |
383 |
2 |
191 |
1 |
153 |
384 |
13 |
29 |
7 |
154 |
391 |
2 |
195 |
1 |
155 |
392 |
17 |
23 |
1 |
156 |
393 |
2 |
196 |
1 |
157 |
394 |
9 |
43 |
7 |
158 |
401 |
2 |
200 |
1 |
159 |
402 |
401 |
1 |
1 |
160 |
403 |
2 |
201 |
1 |
161 |
404 |
199 |
2 |
6 |
162 |
410 |
409 |
1 |
1 |
163 |
411 |
2 |
205 |
1 |
164 |
412 |
3 |
137 |
1 |
165 |
413 |
2 |
206 |
1 |
166 |
414 |
7 |
59 |
1 |
167 |
415 |
2 |
207 |
1 |
168 |
416 |
5 |
83 |
1 |
169 |
417 |
2 |
208 |
1 |
170 |
418 |
3 |
139 |
1 |
171 |
419 |
2 |
209 |
1 |
172 |
420 |
419 |
1 |
1 |
173 |
421 |
2 |
210 |
1 |
174 |
422 |
421 |
1 |
1 |
175 |
423 |
2 |
211 |
1 |
176 |
424 |
3 |
141 |
1 |
177 |
425 |
2 |
212 |
1 |
178 |
426 |
5 |
85 |
1 |
179 |
427 |
2 |
213 |
1 |
180 |
428 |
7 |
61 |
1 |
181 |
429 |
2 |
214 |
1 |
182 |
430 |
3 |
143 |
1 |
183 |
431 |
2 |
215 |
1 |
184 |
432 |
431 |
1 |
1 |
185 |
433 |
2 |
216 |
1 |
186 |
434 |
433 |
1 |
1 |
187 |
435 |
2 |
217 |
1 |
188 |
436 |
3 |
145 |
1 |
189 |
437 |
2 |
218 |
1 |
190 |
438 |
19 |
23 |
1 |
191 |
439 |
2 |
219 |
1 |
192 |
440 |
439 |
1 |
1 |
193 |
441 |
2 |
220 |
1 |
194 |
442 |
3 |
147 |
1 |
195 |
443 |
2 |
221 |
1 |
196 |
444 |
443 |
1 |
1 |
197 |
445 |
439 |
1 |
6 |
198 |
451 |
2 |
225 |
1 |
199 |
452 |
11 |
41 |
1 |
200 |
453 |
2 |
226 |
1 |
201 |
454 |
3 |
151 |
1 |
202 |
455 |
2 |
227 |
1 |
203 |
456 |
11 |
41 |
5 |
204 |
461 |
2 |
230 |
1 |
205 |
462 |
461 |
1 |
1 |
206 |
463 |
2 |
231 |
1 |
207 |
464 |
463 |
1 |
1 |
208 |
465 |
9 |
51 |
6 |
209 |
471 |
2 |
235 |
1 |
210 |
472 |
3 |
157 |
1 |
211 |
473 |
2 |
236 |
1 |
212 |
474 |
11 |
43 |
1 |
213 |
475 |
7 |
67 |
6 |
214 |
481 |
2 |
240 |
1 |
215 |
482 |
13 |
37 |
1 |
216 |
483 |
2 |
241 |
1 |
217 |
484 |
3 |
161 |
1 |
218 |
485 |
479 |
1 |
6 |
219 |
491 |
2 |
245 |
1 |
220 |
492 |
491 |
1 |
1 |
221 |
493 |
2 |
246 |
1 |
222 |
494 |
17 |
29 |
1 |
223 |
495 |
163 |
3 |
6 |
224 |
501 |
2 |
250 |
1 |
225 |
502 |
3 |
167 |
1 |
226 |
503 |
2 |
251 |
1 |
227 |
504 |
503 |
1 |
1 |
228 |
505 |
10 |
50 |
5 |
229 |
510 |
509 |
1 |
1 |
230 |
511 |
2 |
255 |
1 |
231 |
512 |
7 |
73 |
1 |
232 |
513 |
2 |
256 |
1 |
233 |
514 |
3 |
171 |
1 |
234 |
515 |
2 |
257 |
1 |
235 |
516 |
5 |
103 |
1 |
236 |
517 |
2 |
258 |
1 |
237 |
518 |
11 |
47 |
1 |
238 |
519 |
2 |
259 |
1 |
239 |
520 |
3 |
173 |
1 |
240 |
521 |
2 |
260 |
1 |
241 |
522 |
521 |
1 |
1 |
242 |
523 |
2 |
261 |
1 |
243 |
524 |
523 |
1 |
1 |
244 |
525 |
2 |
262 |
1 |
245 |
526 |
3 |
175 |
1 |
246 |
527 |
2 |
263 |
1 |
247 |
528 |
17 |
31 |
1 |
248 |
529 |
2 |
264 |
1 |
249 |
530 |
23 |
23 |
1 |
250 |
531 |
2 |
265 |
1 |
251 |
532 |
3 |
177 |
1 |
252 |
533 |
2 |
266 |
1 |
253 |
534 |
13 |
41 |
1 |
254 |
535 |
2 |
267 |
1 |
255 |
536 |
5 |
107 |
1 |
256 |
537 |
2 |
268 |
1 |
257 |
538 |
3 |
179 |
1 |
258 |
539 |
2 |
269 |
1 |
259 |
540 |
7 |
77 |
1 |
260 |
541 |
2 |
270 |
1 |
261 |
542 |
541 |
1 |
1 |
262 |
543 |
2 |
271 |
1 |
263 |
544 |
3 |
181 |
1 |
264 |
545 |
2 |
272 |
1 |
265 |
546 |
5 |
109 |
1 |
266 |
547 |
2 |
273 |
1 |
267 |
548 |
547 |
1 |
1 |
268 |
549 |
2 |
274 |
1 |
269 |
550 |
3 |
183 |
1 |
270 |
551 |
2 |
275 |
1 |
271 |
552 |
19 |
29 |
1 |
272 |
553 |
2 |
276 |
1 |
273 |
554 |
7 |
79 |
1 |
274 |
555 |
2 |
277 |
1 |
275 |
556 |
19 |
29 |
5 |
276 |
561 |
2 |
280 |
1 |
277 |
562 |
3 |
187 |
1 |
278 |
563 |
2 |
281 |
1 |
279 |
564 |
563 |
1 |
1 |
280 |
565 |
2 |
282 |
1 |
281 |
566 |
5 |
113 |
1 |
282 |
567 |
563 |
1 |
4 |
283 |
571 |
2 |
285 |
1 |
284 |
572 |
571 |
1 |
1 |
285 |
573 |
2 |
286 |
1 |
286 |
574 |
3 |
191 |
1 |
287 |
575 |
2 |
287 |
1 |
288 |
576 |
571 |
1 |
5 |
289 |
581 |
2 |
290 |
1 |
290 |
582 |
7 |
83 |
1 |
291 |
583 |
2 |
291 |
1 |
292 |
584 |
11 |
53 |
1 |
293 |
585 |
2 |
292 |
1 |
294 |
586 |
7 |
83 |
5 |
295 |
591 |
2 |
295 |
1 |
296 |
592 |
3 |
197 |
1 |
297 |
593 |
2 |
296 |
1 |
298 |
594 |
593 |
1 |
1 |
299 |
595 |
2 |
297 |
1 |
300 |
596 |
197 |
3 |
5 |
301 |
601 |
2 |
300 |
1 |
302 |
602 |
601 |
1 |
1 |
303 |
603 |
2 |
301 |
1 |
304 |
604 |
3 |
201 |
1 |
305 |
605 |
2 |
302 |
1 |
306 |
606 |
7 |
86 |
4 |
307 |
610 |
3 |
203 |
1 |
308 |
611 |
2 |
305 |
1 |
309 |
612 |
13 |
47 |
1 |
310 |
613 |
2 |
306 |
1 |
311 |
614 |
613 |
1 |
1 |
312 |
615 |
2 |
307 |
1 |
313 |
616 |
3 |
205 |
1 |
314 |
617 |
2 |
308 |
1 |
315 |
618 |
617 |
1 |
1 |
316 |
619 |
2 |
309 |
1 |
317 |
620 |
619 |
1 |
1 |
318 |
621 |
2 |
310 |
1 |
319 |
622 |
3 |
207 |
1 |
320 |
623 |
2 |
311 |
1 |
321 |
624 |
7 |
89 |
1 |
322 |
625 |
2 |
312 |
1 |
323 |
626 |
5 |
125 |
1 |
324 |
627 |
2 |
313 |
1 |
325 |
628 |
3 |
209 |
1 |
326 |
629 |
2 |
314 |
1 |
327 |
630 |
17 |
37 |
1 |
328 |
631 |
2 |
315 |
1 |
329 |
632 |
631 |
1 |
1 |
330 |
633 |
2 |
316 |
1 |
331 |
634 |
3 |
211 |
1 |
332 |
635 |
2 |
317 |
1 |
333 |
636 |
5 |
127 |
1 |
334 |
637 |
2 |
318 |
1 |
335 |
638 |
7 |
91 |
1 |
336 |
639 |
2 |
319 |
1 |
337 |
640 |
3 |
213 |
1 |
338 |
641 |
2 |
320 |
1 |
339 |
642 |
641 |
1 |
1 |
340 |
643 |
2 |
321 |
1 |
341 |
644 |
643 |
1 |
1 |
342 |
645 |
2 |
322 |
1 |
343 |
646 |
3 |
215 |
1 |
344 |
647 |
2 |
323 |
1 |
345 |
648 |
647 |
1 |
1 |
346 |
649 |
2 |
324 |
1 |
347 |
650 |
11 |
59 |
1 |
348 |
651 |
2 |
325 |
1 |
349 |
652 |
3 |
217 |
1 |
350 |
653 |
2 |
326 |
1 |
351 |
654 |
653 |
1 |
1 |
352 |
655 |
2 |
327 |
1 |
353 |
656 |
5 |
131 |
1 |
354 |
657 |
2 |
328 |
1 |
355 |
658 |
3 |
219 |
1 |
356 |
659 |
2 |
329 |
1 |
357 |
660 |
659 |
1 |
1 |
358 |
661 |
2 |
330 |
1 |
359 |
662 |
661 |
1 |
1 |
360 |
663 |
2 |
331 |
1 |
361 |
664 |
3 |
221 |
1 |
362 |
665 |
2 |
332 |
1 |
363 |
666 |
5 |
133 |
1 |
364 |
667 |
13 |
51 |
4 |
365 |
671 |
2 |
335 |
1 |
366 |
672 |
11 |
61 |
1 |
367 |
673 |
2 |
336 |
1 |
368 |
674 |
673 |
1 |
1 |
369 |
675 |
2 |
337 |
1 |
370 |
676 |
3 |
225 |
1 |
371 |
677 |
2 |
338 |
1 |
372 |
678 |
5 |
135 |
3 |
373 |
681 |
2 |
340 |
1 |
374 |
682 |
3 |
227 |
1 |
375 |
683 |
2 |
341 |
1 |
376 |
684 |
683 |
1 |
1 |
377 |
685 |
2 |
342 |
1 |
378 |
686 |
5 |
137 |
1 |
379 |
687 |
683 |
1 |
4 |
380 |
691 |
2 |
345 |
1 |
381 |
692 |
691 |
1 |
1 |
382 |
693 |
2 |
346 |
1 |
383 |
694 |
3 |
231 |
1 |
384 |
695 |
2 |
347 |
1 |
385 |
696 |
5 |
139 |
1 |
386 |
697 |
7 |
99 |
4 |
387 |
701 |
2 |
350 |
1 |
388 |
702 |
701 |
1 |
1 |
389 |
703 |
2 |
351 |
1 |
390 |
704 |
19 |
37 |
1 |
391 |
705 |
2 |
352 |
1 |
392 |
706 |
3 |
235 |
1 |
393 |
707 |
4 |
176 |
3 |
394 |
710 |
709 |
1 |
1 |
395 |
711 |
2 |
355 |
1 |
396 |
712 |
3 |
237 |
1 |
397 |
713 |
2 |
356 |
1 |
398 |
714 |
23 |
31 |
1 |
399 |
715 |
2 |
357 |
1 |
400 |
716 |
5 |
143 |
1 |
401 |
717 |
2 |
358 |
1 |
402 |
718 |
3 |
239 |
1 |
403 |
719 |
2 |
359 |
1 |
404 |
720 |
719 |
1 |
1 |
405 |
721 |
2 |
360 |
1 |
406 |
722 |
7 |
103 |
1 |
407 |
723 |
2 |
361 |
1 |
408 |
724 |
3 |
241 |
1 |
409 |
725 |
2 |
362 |
1 |
410 |
726 |
5 |
145 |
1 |
411 |
727 |
2 |
363 |
1 |
412 |
728 |
727 |
1 |
1 |
413 |
729 |
2 |
364 |
1 |
414 |
730 |
3 |
243 |
1 |
415 |
731 |
2 |
365 |
1 |
416 |
732 |
17 |
43 |
1 |
417 |
733 |
2 |
366 |
1 |
418 |
734 |
733 |
1 |
1 |
419 |
735 |
2 |
367 |
1 |
420 |
736 |
3 |
245 |
1 |
421 |
737 |
2 |
368 |
1 |
422 |
738 |
11 |
67 |
1 |
423 |
739 |
2 |
369 |
1 |
424 |
740 |
739 |
1 |
1 |
425 |
741 |
2 |
370 |
1 |
426 |
742 |
3 |
247 |
1 |
427 |
743 |
2 |
371 |
1 |
428 |
744 |
743 |
1 |
1 |
429 |
745 |
2 |
372 |
1 |
430 |
746 |
5 |
149 |
1 |
431 |
747 |
2 |
373 |
1 |
432 |
748 |
3 |
249 |
1 |
433 |
749 |
2 |
374 |
1 |
434 |
750 |
7 |
107 |
1 |
435 |
751 |
2 |
375 |
1 |
436 |
752 |
751 |
1 |
1 |
437 |
753 |
2 |
376 |
1 |
438 |
754 |
3 |
251 |
1 |
439 |
755 |
2 |
377 |
1 |
440 |
756 |
5 |
151 |
1 |
441 |
757 |
2 |
378 |
1 |
442 |
758 |
757 |
1 |
1 |
443 |
759 |
2 |
379 |
1 |
444 |
760 |
3 |
253 |
1 |
445 |
761 |
2 |
380 |
1 |
446 |
762 |
761 |
1 |
1 |
447 |
763 |
2 |
381 |
1 |
448 |
764 |
7 |
109 |
1 |
449 |
765 |
2 |
382 |
1 |
450 |
766 |
3 |
255 |
1 |
451 |
767 |
2 |
383 |
1 |
452 |
768 |
13 |
59 |
1 |
453 |
769 |
2 |
384 |
1 |
454 |
770 |
769 |
1 |
1 |
455 |
771 |
2 |
385 |
1 |
456 |
772 |
3 |
257 |
1 |
457 |
773 |
2 |
386 |
1 |
458 |
774 |
773 |
1 |
1 |
459 |
775 |
2 |
387 |
1 |
460 |
776 |
5 |
155 |
1 |
461 |
777 |
2 |
388 |
1 |
462 |
778 |
5 |
155 |
3 |
463 |
781 |
2 |
390 |
1 |
464 |
782 |
11 |
71 |
1 |
465 |
783 |
2 |
391 |
1 |
466 |
784 |
3 |
261 |
1 |
467 |
785 |
2 |
392 |
1 |
468 |
786 |
5 |
157 |
1 |
469 |
787 |
2 |
393 |
1 |
470 |
788 |
787 |
1 |
1 |
471 |
789 |
787 |
1 |
2 |
472 |
791 |
2 |
395 |
1 |
473 |
792 |
7 |
113 |
1 |
474 |
793 |
2 |
396 |
1 |
475 |
794 |
13 |
61 |
1 |
476 |
795 |
2 |
397 |
1 |
477 |
796 |
3 |
265 |
1 |
478 |
797 |
2 |
398 |
1 |
479 |
798 |
5 |
159 |
3 |
480 |
801 |
2 |
400 |
1 |
481 |
802 |
3 |
267 |
1 |
482 |
803 |
2 |
401 |
1 |
483 |
804 |
11 |
73 |
1 |
484 |
805 |
2 |
402 |
1 |
485 |
806 |
5 |
161 |
1 |
486 |
807 |
2 |
403 |
1 |
487 |
808 |
13 |
62 |
2 |
488 |
810 |
809 |
1 |
1 |
489 |
811 |
2 |
405 |
1 |
490 |
812 |
811 |
1 |
1 |
491 |
813 |
2 |
406 |
1 |
492 |
814 |
3 |
271 |
1 |
493 |
815 |
2 |
407 |
1 |
494 |
816 |
5 |
163 |
1 |
495 |
817 |
2 |
408 |
1 |
496 |
818 |
19 |
43 |
1 |
497 |
819 |
2 |
409 |
1 |
498 |
820 |
3 |
273 |
1 |
499 |
821 |
2 |
410 |
1 |
500 |
822 |
821 |
1 |
1 |