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

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Oct 31 2002

Keywords

• nonn
• base

Comments

a(A018826(n))>0; is a(n)<=1 for all n?

Not multiplicative: a(5) = 0, a(29) = 0, a(145) = 1. - David W. Wilson, Jun 10 2005

a(n) <= 1 for n <= 10^6. - Robert Israel, Jul 11 2018

Examples

			a(27) = 1 as 27 = '11011' occurs in 27^2=729 = '1011011001' once: '**11011***'.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A018826.

Programs

Maple

f:= proc(n) local S,S2;
    S:= convert(convert(n,binary),string);
    S2:= convert(convert(n^2,binary),string);
    nops([StringTools:-SearchAll(S,S2)])
end proc:
map(f, [$0..200]); # Robert Israel, Jul 11 2018

PARI

issub(b, bs, k) = {for (i=1, #b, if (b[i] != bs[i+k-1], return (0));); return (1);}
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