cp's OEIS Frontend

A076141 Number of times n occurs as a binary sub-pattern of n^2.

%I A076141 #21 Jul 11 2018 20:12:54
%S A076141 1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,
%T A076141 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,
%U A076141 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A076141 Number of times n occurs as a binary sub-pattern of n^2.
%C A076141 a(A018826(n))>0; is a(n)<=1 for all n?
%C A076141 Not multiplicative: a(5) = 0, a(29) = 0, a(145) = 1. - _David W. Wilson_, Jun 10 2005
%C A076141 a(n) <= 1 for n <= 10^6. - _Robert Israel_, Jul 11 2018
%H A076141 Robert Israel, <a href="/A076141/b076141.txt">Table of n, a(n) for n = 0..10000</a>
%e A076141 a(27) = 1 as 27 = '11011' occurs in 27^2=729 = '1011011001' once: '**11011***'.
%p A076141 f:= proc(n) local S,S2;
%p A076141     S:= convert(convert(n,binary),string);
%p A076141     S2:= convert(convert(n^2,binary),string);
%p A076141     nops([StringTools:-SearchAll(S,S2)])
%p A076141 end proc:
%p A076141 map(f, [$0..200]); # _Robert Israel_, Jul 11 2018
%o A076141 (PARI) issub(b, bs, k) = {for (i=1, #b, if (b[i] != bs[i+k-1], return (0));); return (1);}
%o A076141 a(n) = {if (n, b = binary(n), b = [0]); if (n, bs = binary(n^2), bs = [0]); sum(k=1, #bs - #b +1, issub(b, bs, k));} \\ _Michel Marcus_, Mar 15 2015
%Y A076141 Cf. A018826.
%K A076141 nonn,base
%O A076141 0,1
%A A076141 _Reinhard Zumkeller_, Oct 31 2002