A103671 Smallest m such that the binary representation of n! does not contain m!.

4, 5, 5, 5, 6, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 5, 6, 5, 6, 5, 6, 5, 5, 5, 6, 6, 6, 5, 7, 6, 6, 6, 6, 6, 7, 6, 6, 5, 6, 6, 6, 6, 6, 6, 5, 6, 7, 6, 6, 5, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 7, 6, 6

Offset

6,1

Comments

Reinhard Zumkeller conjectures (at A102730) that this sequence is bounded. I conjecture the contrary, that for every k there is n with a(n) > k. - Charles R Greathouse IV, Apr 07 2013

Links

Amiram Eldar, Table of n, a(n) for n = 6..10000

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to factorial numbers.

Mathematica

q[n_, m_] := StringContainsQ[IntegerString[n!, 2], IntegerString[m!, 2]]; a[n_] := Module[{m = 2}, While[q[n, m], m++]; m]; Array[a, 105, 6] (* Amiram Eldar, Apr 03 2025 *)

Crossrefs

Cf. A102730, A103672, A036603, A007088, A000142.

Sequence in context: A117768 A018245 A264936 * A144192 A029909 A141276

Adjacent sequences: A103668 A103669 A103670 * A103672 A103673 A103674

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 12 2005

Status

approved