A094009 Least number k such that k! in binary representation contains a run of exactly n consecutive ones.

1, 3, 7, 5, 10, 12, 33, 38, 47, 39, 67, 37, 120, 71, 189, 568, 119, 411, 952, 909, 1438, 1215, 2107, 3435, 10644, 4390, 19154, 12144, 21458, 27294, 54773, 104306, 115552, 46620, 112657, 100468, 252543, 374264, 467532, 582700

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Example

a(4) = 5 because 5! = 1111000_b.

Mathematica

helper[b_][a : {b_, ___}] := Length[a]; helper[b_][a_List] := 0; maxConsecutiveCount[m_List, x_] := Max[helper[x] /@ Split[m]] (* Bobby R. Treat (drbob(AT)bigfoot.com), Apr 20 2004 *)
a = Table[0, {30}]; Do[ b = maxConsecutiveCount[ IntegerDigits[n!, 2], 1]; If[ a[[b]] == 0, a[[b]] = n], {n, 17500}]; a

Crossrefs

Cf. A094010.

Sequence in context: A264983 A265341 A358793 * A328185 A349772 A088514

Adjacent sequences: A094006 A094007 A094008 * A094010 A094011 A094012

Keyword

nonn,base,more

Author

Robert G. Wilson v, Apr 20 2004

Extensions

a(27)-a(29) from Bobby R. Treat, Apr 21 2004

a(30)-a(36) from Robert G. Wilson v, Aug 18 2010

a(37)-a(40) and name clarified from Michael S. Branicky, Jan 17 2025

Status

approved