Thread: burmuda triangle strikes again

Forget this. It's a weird double-post accident....

A very straightforward way of doing it:

Code:

#include <stdio.h>
#include <stdlib.h>
 
#define LIMIT 10000000000000000000u // ten quintillion
 
int main() {
    unsigned long a[20];
    unsigned n = 0, size = sizeof a / sizeof *a;
 
    unsigned long tri  = 1, tri_add  = 2, tri_delta  = 1,
                  pent = 1, pent_add = 4, pent_delta = 3;
    unsigned tri_ind = 1, pent_ind = 1;

    printf("triangular and pentagonal:\n");
 
    while (pent < LIMIT) {
        while (tri < pent) {
            tri += tri_add; tri_add += tri_delta; ++tri_ind;
        }
 
        if (tri == pent) {
            printf("%19lu (%10u, %10u)\n", tri, tri_ind, pent_ind);
            if (n >= size) { printf("array overflow\n"); exit(1); }
            a[n++] = tri;
            tri += tri_add; tri_add += tri_delta; ++tri_ind;
        }
 
        while (pent < tri) {
            pent += pent_add; pent_add += pent_delta; ++pent_ind;
        }
 
        if (tri == pent) {
            printf("%19lu (%10u, %10u)\n", tri, tri_ind, pent_ind);
            if (n >= size) { printf("array overflow\n"); exit(1); }
            a[n++] = tri;
            pent += pent_add; pent_add += pent_delta; ++pent_ind;
        }
    }
 
    printf("\nalso hexagonal:\n");
 
    unsigned long hex = 1, hex_add = 5, hex_delta = 4;
    unsigned hex_ind = 1;
 
    for (unsigned i = 0; i < n; ) {
        while (hex < a[i]) {
            hex += hex_add; hex_add += hex_delta; ++hex_ind;
        }
        if (hex == a[i]) printf("%19lu (%10u)\n", hex, hex_ind);
        ++i;
        hex += hex_add; hex_add += hex_delta; ++hex_ind;
    }
 
    return 0;
}

Output:

triangular and pentagonal:
                  1 (         1,          1)
                210 (        20,         12)
              40755 (       285,        165)
            7906276 (      3976,       2296)
         1533776805 (     55385,      31977)
       297544793910 (    771420,     445380)
     57722156241751 (  10744501,    6203341)
  11197800766105800 ( 149651600,   86401392)
2172315626468283465 (2084377905, 1203416145)

also hexagonal:
                  1 (         1)
              40755 (       143)
         1533776805 (     27693)
     57722156241751 (   5372251)
2172315626468283465 (1042188953)

So every second number that is both triangular and pentagonal is also hexagonal.