A232608 Triangular numbers t such that distances from t to three nearest squares are three triangular numbers.

1, 10, 15, 253, 325, 11026, 237016, 8439886, 1119946128

Offset

1,2

Comments

Triangular numbers in A232501.

Links

Table of n, a(n) for n=1..9.

Prog

(C99)
#include <stdio.h>
#include <math.h>
typedef unsigned long long U64;
int isTriang(U64 x) {
    x+=x;
    U64 r = sqrt(x);
    return (r*(r+1)==x);
}
int main() {
  for (U64 n=0, i=0; i < (1ULL<<32); ++i) {
    U64 s, d, d1, d2, d3;
    s = sqrt(n+=i);
    d1 = n - s*s;
    if (!isTriang(d1)) continue;
    d2 = (s+1)*(s+1) - n;
    if (!isTriang(d2)) continue;
    d3 = (s+2)*(s+2) - n;
    if (s) {
        d = n - (s-1)*(s-1);
        if (d < d3)  d3 = d;
    }
    if (isTriang(d3))   printf("%llu, ", n);
  }
}
(Haskell)
a232608 n = a232608_list !! (n-1)
a232608_list = filter f $ tail a000217_list where
   f x = all ((== 1) . a010054) $ init $ sort $
         map (abs . (x -) . (^ 2) . (+ (a000196 x))) [-1..2]
-- Reinhard Zumkeller, Mar 16 2014

Crossrefs

Cf. A000217, A000290, A232501.

Cf. A000196, A010054.

Sequence in context: A278349 A114703 A134515 * A175335 A167788 A341012

Adjacent sequences: A232605 A232606 A232607 * A232609 A232610 A232611

Keyword

nonn,hard,more

Author

Alex Ratushnyak, Feb 23 2014

Status

approved