A072521 a(1) = 6 and then the smallest triangular numbers such that sum of two neighbors is also a triangular number.

6, 15, 21, 45, 91, 990, 1711, 365085, 401856, 713415, 785631, 1079715, 1326006, 2355535, 2888406, 5137615, 5666661, 5764710, 9550635, 9921285, 10934826, 19434495, 21421785, 23622501, 42003195, 46315500, 82349361, 146384605

Offset: 1

Author

Amarnath Murthy, Jul 31 2002

Keywords

• nonn

Comments

The sequence is unbounded as a(n+1) is less than or equal to the n-th triangular number.

Examples

			45 is a term because 21 + 45 = 66, 45 + 91 = 136, and 66 and 136 are triangular numbers.
		

Crossrefs

Cf. A072522.

Programs

PARI

p=6; k=3; print1(p", "); for(n=1, 30, k=k+1; u=p+k*(k+1)/2; t=floor(sqrt(2*u)); while(u!=t*(t+1)/2, k=k+1; u=p+k*(k+1)/2; t=floor(sqrt(2*u))); p=k*(k+1)/2; print1(p", "))

Extensions

More terms from Ralf Stephan, Mar 30 2003