A103674 - OEIS

%I #16 Apr 07 2013 08:25:13

%S 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,

%T 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,

%U 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

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

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

%C Conjecture: a(n) = 1 for n > 802. - _Charles R Greathouse IV_, Apr 07 2013

%C Conjecture checked up to n <= 5*10^5. - _Giovanni Resta_, Apr 07 2013

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%o (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

%Y Cf. A102730, A036603, A007088, A000142, A103673, A103675.

%K nonn,base

%O 0,1

%A _Reinhard Zumkeller_, Feb 12 2005