A103674 If in binary representation n! contains 6! then 1 else 0.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

Offset: 0

Author

Reinhard Zumkeller, Feb 12 2005

Keywords

• nonn
• base

Comments

Conjecture: a(n) = 1 for n > 802. - Charles R Greathouse IV, Apr 07 2013

Conjecture checked up to n <= 5*10^5. - Giovanni Resta, Apr 07 2013

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1000
• Index entries for characteristic functions.
• Index entries for sequences related to factorial numbers.
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A000142, A007088, A036603, A102730, A103673, A103675, A103678, A103679.

Programs

PARI

a(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

Formula

a(A103678(n)) = 1, a(A103679(n)) = 0.