A354301 Numbers k such that k!, (k+1)! and (k+2)! have the same binary weight (A000120).
0, 7, 12, 262, 12887667
Offset: 1
Examples
7 is a term since A079584(7) = A079584(8) = A079584(9) = 6. 12 is a term since A079584(12) = A079584(13) = A079584(14) = 12.
Programs
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Mathematica
s[n_] := s[n] = DigitCount[n!, 2, 1]; Select[Range[0, 300], s[#] == s[# + 1] == s[# + 2] &]
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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, fn1, fn2, wtn, wtn1, wtn2 = 0, 1, 1, 2, 1, 1, 1 for n in count(0): if wtn == wtn1 == wtn2: yield n fn, fn1, fn2 = fn1, fn2, fn2*(n+3) wtn, wtn1, wtn2 = wtn1, wtn2, wt(fn2) print(list(islice(agen(), 4))) # Michael S. Branicky, May 23 2022
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