OFFSET
1,1
COMMENTS
Theorem (by Ivan N. Ianakiev): There are infinitely many such numbers. Proof: Any triangular number of the form A000217(n^2) for n>1 is such a number, as A000217(n^2) = A000217(n^2-1) + A000290(n), for n>=1. Observation: Other numbers not of the form A000217(n^2), for example 15 and 28, are also in A182427. - Ivan N. Ianakiev, May 30 2012
For any integer k>1, all triangular numbers with indices of the form 3*k-2 (A060544) are terms as (3*k-2)*(3*k-1)/2 = (2*k-1)^2 + (k-1)*k/2. - Ivan N. Ianakiev, Nov 25 2015
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
EXAMPLE
10, 15, 28 are in the sequence because 10 = 2^2 + 3*4/2 = 3^2 + 1*2/2, 15 = 3^2 + 3*4/2, 28 = 5^2 + 2*3/2.
PROG
(PARI) isok(t) = {for (k=1, sqrtint(t), my(tt = t - k^2); if ((tt) && ispolygonal(tt, 3), return (1)); ); }
lista(nn) = {for (n=1, nn, my(t = n*(n+1)/2); if (isok(t), print1(t, ", ")); ); } \\ Michel Marcus, Nov 25 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Ivan N. Ianakiev, Apr 28 2012
STATUS
approved