A103679 Numbers m such that the binary representation of m! does not contain 6!.

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 56, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 72, 73, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 87

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2005

Keywords

• nonn
• base

Comments

Last term is probably 802. No numbers between 803 and 500000 belong to the sequence. - Giovanni Resta, Apr 07 2013

Links

• Amiram Eldar, Table of n, a(n) for n = 1..167
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to factorial numbers.

Crossrefs

Complement of A103678.

Cf. A000142, A007088, A036603, A102730, A103674, A103677, A103680, A103681.

Programs

Mathematica

Select[Range[0,100],SequenceCount[IntegerDigits[#!,2],{1,0,1,1,0,1,0,0,0,0}]==0&] (* Harvey P. Dale, Oct 12 2024 *)

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(0))); 1 \\ Charles R Greathouse IV, Apr 07 2013

Formula

A103674(a(n)) = 0, A103674(A103678(n)) = 1.