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

Author

Reinhard Zumkeller, Feb 12 2005

Keywords

• nonn
• base

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.

Crossrefs

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

Programs

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 *)

Formula

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