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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A185096

Adjacent sequences:  A226833 A226834 A226835 * A226837 A226838 A226839

KEYWORD

nonn,base,less

AUTHOR

Alex Ratushnyak, Jun 19 2013

STATUS

approved

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Last modified February 28 10:20 EST 2020. Contains 332323 sequences. (Running on oeis4.)