cp's OEIS Frontend

A226836 Squares s such that first m and last m digits of the binary representation are perfect positive squares written in binary, and m = floor(binaryLength(s)/2), where binaryLength(s) = A070939(s) is the binary length of s.

%I A226836 #5 Jul 01 2013 13:40:38
%S A226836 36,289,4624,10404,115600,248004,1083681,1281424,2232036,2509056,
%T A226836 21307456,23892544,31494544,40144896,66357316,271359729,340919296,
%U A226836 479785216,512026384,597215844,767068416,4831918144,5454708736,8126661904,8522982400,12273094656,16705045504
%N A226836 Squares s such that first m and last m digits of the binary representation are perfect positive squares written in binary, and m = floor(binaryLength(s)/2), where binaryLength(s) = A070939(s) is the binary length of s.
%C A226836 The sequence of roots of a(n) begins: 6, 17, 68, 102, 340, 498, 1041, 1132, 1494, 1584, 4616, 4888, 5612, 6336, 8146, 16473, 18464, 21904, 22628, 24438, 27696, 69512, 73856, 90148, 92320, ...
%o A226836 (C)
%o A226836 #include <stdio.h>
%o A226836 #include <math.h>
%o A226836 typedef unsigned long long U64;
%o A226836 U64 isSquare(U64 a) {
%o A226836     U64 s = sqrt(a);
%o A226836     return (s*s==a);
%o A226836 }
%o A226836 int main() {
%o A226836   U64 i, j, n, sq, s, S;
%o A226836   for (n = 1; n < (1ULL<<20); ++n) {
%o A226836     for (i = 64, j = sq = n*n; j < (1ULL<<63); j += j)
%o A226836       --i;  // binary length of sq
%o A226836     j = i >> 1;  //  Sbs or Ss, binary length of s is j
%o A226836     s = sq & ((1ULL<<j)-1);
%o A226836     S = sq >> (j+(i&1));
%o A226836     if (isSquare(S) && s && isSquare(s)) printf("%llu, ", sq);
%o A226836   }
%o A226836   return 0;
%o A226836 }
%Y A226836 Cf. A070939, A226736.
%K A226836 nonn,base,less
%O A226836 1,1
%A A226836 _Alex Ratushnyak_, Jun 19 2013