A103672 Greatest m < n such that the binary representation of n! contains m!.

0, 1, 2, 3, 4, 3, 4, 7, 4, 5, 4, 5, 4, 4, 4, 15, 4, 4, 4, 6, 4, 5, 6, 4, 5, 4, 5, 4, 5, 6, 6, 31, 5, 5, 5, 4, 6, 5, 5, 5, 5, 5, 6, 5, 5, 4, 5, 5, 5, 5, 5, 5, 6, 5, 6, 5, 5, 6, 5, 5, 5, 5, 5, 63, 6, 5, 5, 5, 5, 5, 6, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 6, 6, 5, 5, 5, 6, 7, 5, 6, 5, 5

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to factorial numbers.

Formula

a(2^k) = 2^k - 1, a(A000079(k)) = A000225(k).

Mathematica

q[n_, m_] := StringContainsQ[IntegerString[n!, 2], IntegerString[m!, 2]]; a[n_] := Module[{m = n-1}, While[!q[n, m], m--]; m]; Array[a, 104] (* Amiram Eldar, Apr 03 2025 *)

Crossrefs

Cf. A000079, A000225, A102730, A103671, A036603, A007088, A000142.

Sequence in context: A177329 A360379 A253852 * A309255 A375290 A201443

Adjacent sequences: A103669 A103670 A103671 * A103673 A103674 A103675

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 12 2005

Status

approved