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A226836
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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PROG
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(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;
}
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CROSSREFS
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KEYWORD
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nonn,base,less
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AUTHOR
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STATUS
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approved
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