

A234336


Triangular numbers t such that both distances from t to two nearest squares are perfect squares.


1



0, 1, 45, 153, 325, 10440, 1385280, 2530125, 145462096, 253472356000, 896473314291600, 18598323060963360, 4923539323344237960, 27021247523935843321, 1779312917089890560241, 2355054824151326520405, 21328127890911040269960, 124797500891024855239125
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OFFSET

1,3


COMMENTS

Except a(1)=0, a(n) are triangular numbers t such that both tx and yt are perfect squares, where x and y are two nearest to k squares: x < t <= y.
The sequence of k's such that triangular(k) is in A234334 begins: 0, 1, 9, 17, 25, 144, 1664, 2249, 17056, 712000, ...


LINKS



EXAMPLE

Triangular(9) = 45 is in the sequence because both 4536=9 and 4945=4 are perfect squares, where 36 and 49 are the two squares nearest to 45.


PROG

(C)
#include <stdio.h>
#include <math.h>
typedef unsigned long long U64;
U64 isSquare(U64 a) {
U64 r = sqrt(a);
return r*r==a;
}
int main() {
for (U64 i=0; i<(1ULL<<32); ++i) {
U64 n = i*(i+1)/2, r = sqrt(n);
if (r*r==n && n) r;
if (isSquare(nr*r) && isSquare((r+1)*(r+1)n))
printf("%llu, ", n);
}
return 0;
}


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



