A234336 - OEIS

A234336

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

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

Triangular numbers in A234334.

Except a(1)=0, a(n) are triangular numbers t such that both t-x and y-t 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

Table of n, a(n) for n=1..18.

EXAMPLE

Triangular(9) = 45 is in the sequence because both 45-36=9 and 49-45=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(n-r*r) && isSquare((r+1)*(r+1)-n))

printf("%llu, ", n);

}

return 0;

}

CROSSREFS

Cf. A000217, A000290, A229909, A234334.

Sequence in context: A044758 A053743 A347874 * A173371 A288669 A305069

Adjacent sequences: A234333 A234334 A234335 * A234337 A234338 A234339

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Dec 23 2013

STATUS

approved