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.

36, 289, 4624, 10404, 115600, 248004, 1083681, 1281424, 2232036, 2509056, 21307456, 23892544, 31494544, 40144896, 66357316, 271359729, 340919296, 479785216, 512026384, 597215844, 767068416, 4831918144, 5454708736, 8126661904, 8522982400, 12273094656, 16705045504

Offset

1,1

Comments

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, ...

Links

Table of n, a(n) for n=1..27.

Prog

(C)
#include <stdio.h>
#include <math.h>
typedef unsigned long long U64;
U64 isSquare(U64 a) {
    U64 s = sqrt(a);
    return (s*s==a);
}
int main() {
  U64 i, j, n, sq, s, S;
  for (n = 1; n < (1ULL<<20); ++n) {
    for (i = 64, j = sq = n*n; j < (1ULL<<63); j += j)
      --i;  // binary length of sq
    j = i >> 1;  //  Sbs or Ss, binary length of s is j
    s = sq & ((1ULL<<j)-1);
    S = sq >> (j+(i&1));
    if (isSquare(S) && s && isSquare(s)) printf("%llu, ", sq);
  }
  return 0;
}

Crossrefs

Cf. A070939, A226736.

Sequence in context: A288963 A091081 A017462 * A218647 A067741 A374503

Adjacent sequences: A226833 A226834 A226835 * A226837 A226838 A226839

Keyword

nonn,base,less

Author

Alex Ratushnyak, Jun 19 2013

Status

approved