A354300 Numbers k such that k! and (k+1)! have the same binary weight (A000120).
0, 1, 3, 5, 7, 8, 12, 13, 15, 31, 63, 88, 127, 129, 131, 244, 255, 262, 263, 288, 300, 344, 511, 793, 914, 1012, 1023, 1045, 1116, 1196, 1538, 1549, 1565, 1652, 1817, 1931, 1989, 2047, 2067, 2096, 2459, 2548, 2862, 2918, 2961, 3372, 3478, 3540, 3588, 3673, 3707
Offset: 1
Examples
1 is a term since A079584(1) = A079584(2) = 1. 3 is a term since A079584(3) = A079584(4) = 2.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
s[n_] := s[n] = DigitCount[n!, 2, 1]; Select[Range[0, 4000], s[#] == s[# + 1] &]
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PARI
isok(k) = hammingweight(k!) == hammingweight((k+1)!); \\ Michel Marcus, May 23 2022
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Python
from itertools import count, islice def wt(n): return bin(n).count("1") def agen(): # generator of terms n, fn, fnplus, wtn, wtnplus = 0, 1, 1, 1, 1 for n in count(0): if wtn == wtnplus: yield n fn, fnplus = fnplus, fnplus*(n+2) wtn, wtnplus = wtnplus, wt(fnplus) print(list(islice(agen(), len(data)))) # Michael S. Branicky, May 23 2022
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