A175356 Those positive integers n where, when written in binary, there are exactly k number of runs (of either 0's or 1's) each of exactly k length, for all k where 1<=k<=m, for some positive integer m.
1, 19, 25, 27, 8984, 8988, 9016, 9100, 9112, 9116, 9784, 10008, 10012, 10040, 12568, 12572, 12600, 12680, 12686, 12728, 12740, 12742, 12744, 12750, 12760, 12764, 12856, 13192, 13198, 13240, 13880, 14104, 14108, 14136, 14476, 14488, 14492, 14532, 14534, 14536
Offset: 1
Examples
9016 in binary is 10001100111000. There is exactly one run of one binary digit, two runs of two binary digits, and three runs of three binary digits. (Note that it doesn't matter if the runs are of 0's or of 1's.) So, 9016 is in the sequence.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..12664
- Rémy Sigrist, PARI program for A175356
Programs
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PARI
\\ See Links section.
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Python
from itertools import groupby def ok(n): runlens = [len(list(g)) for k, g in groupby(bin(n)[2:])] return all(runlens.count(k) == k for k in range(1, max(runlens)+1)) def aupto(limit): return [m for m in range(1, limit+1) if ok(m)] print(aupto(14536)) # Michael S. Branicky, Jan 19 2021
Extensions
More terms from Rémy Sigrist, Feb 06 2019
Comments