A094010 Least number k such that k! in binary representation has 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

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Formula

Eliminate the trailing (least significant) trivial zeros by dividing n! by the 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!_d = 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]] (from 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

Author

Robert G. Wilson v, Apr 20 2004

Status

approved