A103675 a(n) = 1 if the binary representation of n! contains 7! (bit string "1001110110000"), otherwise a(n) = 0.

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

Offset: 0

Author

Reinhard Zumkeller, Feb 12 2005

Keywords

• base
• nonn

Comments

a(A103680(n)) = 1, a(A103681(n)) = 0.

Probably a(5153) is the last zero term. a(n) = 1 for n from 5154 to 5*10^5. - Giovanni Resta, Apr 07 2013

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• 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, A102730, A036603, A103673, A103674.

Programs

PARI

a(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

Extensions

Name edited by Antti Karttunen, Dec 24 2018