A094010 Least number k such that k! in binary representation contains a run of exactly n consecutive nontrivial zeros.

6, 7, 9, 11, 15, 19, 40, 54, 38, 67, 63, 56, 37, 69, 352, 236, 258, 600, 1234, 979, 901, 3384, 2268, 4675, 5087, 5820, 3184, 12294, 41082, 25557, 46875, 47107, 67962, 80105, 135854, 195035, 96478, 356975, 424179, 798921, 353800, 547828

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Formula

Eliminate the trailing (least significant) trivial zeros by dividing n! by 2^(Sum_{e=1..max} floor(n/2^e)), max is the first exponent where 2^e >= n. See A011371.

Example

a(4) = 11 because 11! = 10011000010001010100000000_b. The last zeros are trivial.

Mathematica

helper[b_][a : {b_, ___}] := Length[a]; helper[b_][a_List] := 0; maxConsecutiveCount[m_List, x_] := Max[helper[x] /@ Split[m]] (* Dr. Bob drbob(AT)bigfoot.com Apr 20 2004 *)
a = Table[0, {30}]; Do[ b = maxConsecutiveCount[ IntegerDigits[ n! / 2^IntegerExponent[n!, 2], 2], 0]; If[ a[[b]] == 0, a[[b]] = n; Print[b, " = ", n]], {n, 16500}]; a

Crossrefs

Cf. A094009, A011371.

Sequence in context: A074898 A258153 A175221 * A100348 A240882 A241266

Adjacent sequences: A094007 A094008 A094009 * A094011 A094012 A094013

Keyword

nonn,base,more

Author

Robert G. Wilson v, Apr 20 2004

Extensions

a(31)-a(39) and name clarified from Michael S. Branicky, Jan 15 2025

a(40)-a(42) from Michael S. Branicky, Jan 19 2025

Status

approved