A103680 Numbers m such that the binary representation of m! contains 7!.

7, 8, 100, 113, 117, 123, 136, 145, 155, 156, 163, 165, 168, 179, 186, 203, 245, 247, 248, 259, 265, 275, 283, 289, 293, 294, 296, 305, 307, 309, 311, 318, 328, 330, 341, 342, 343, 346, 352, 355, 360, 375, 384, 386, 399, 402, 405, 408, 410, 413, 415, 419

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2005

Keywords

• base
• nonn

Comments

All the numbers from 5154 to 5*10^5 belong to the sequence. - Giovanni Resta, Apr 07 2013

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

Complement of A103681.

Cf. A000142, A007088, A036603, A102730, A103676, A103678, A103679.

Programs

Mathematica

Select[Range[0, 420], StringContainsQ[IntegerString[#!, 2], IntegerString[7!, 2]] &] (* Amiram Eldar, Apr 03 2025 *)

PARI

is(n)=n=n!; while(n>5039, my(e=valuation(n, 2), e1=valuation((n>>=e)+1, 2)); n>>=e1; if(e>3 && e1==2 && bitand(n, 127)==78, return(1))); 0 \\ Charles R Greathouse IV, Apr 07 2013

Formula

A103675(a(n)) = 1, A103675(A103681(n)) = 0.