A103678 Numbers m such that in binary representation m! contains 6!.

6, 20, 23, 30, 31, 32, 37, 43, 53, 55, 58, 65, 71, 74, 81, 86, 91, 94, 95, 99, 102, 106, 108, 111, 115, 116, 117, 118, 122, 123, 124, 127, 128, 129, 133, 134, 135, 139, 141, 143, 144, 145, 149, 153, 155, 157, 158, 159, 160, 162, 163, 166, 167, 168, 169, 170, 171

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2005

Keywords

• nonn
• base

Comments

Complement of A103679: A103674(a(n))=1, A103674(A103679(n))=0.

All the numbers 803 <= n <= 500000 are in the sequence. - Giovanni Resta, Apr 07 2013

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to factorial numbers
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A102730, A036603, A007088, A000142, A103676, A103680.

Programs

Mathematica

With[{c=IntegerDigits[6!,2]},Select[Range[180],SequenceCount[ IntegerDigits[ #!,2], c]>0&]] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Jul 26 2016 *)

PARI

is(n)=n=n!; while(n>719, my(e=valuation(n, 2), e1=valuation((n>>=e)+1, 2)); n>>=e1; if(e>3 && e1==1 && bitand(n, 31)==22, return(1))); 0 \\ Charles R Greathouse IV, Apr 07 2013