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%I #10 Feb 26 2015 15:31:34
%S 6,15,21,45,91,990,1711,365085,401856,713415,785631,1079715,1326006,
%T 2355535,2888406,5137615,5666661,5764710,9550635,9921285,10934826,
%U 19434495,21421785,23622501,42003195,46315500,82349361,146384605
%N a(1) = 6 and then the smallest triangular numbers such that sum of two neighbors is also a triangular number.
%C The sequence is unbounded as a(n+1) is less than or equal to the n-th triangular number.
%e 45 is a term because 21 + 45 = 66, 45 + 91 = 136, and 66 and 136 are triangular numbers.
%o (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", "))
%Y Cf. A072522.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Jul 31 2002
%E More terms from _Ralf Stephan_, Mar 30 2003
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