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%I #12 May 13 2023 19:12:19
%S 0,2,5,189,3074,218685
%N Numbers n such that triangular(n)+1 is a square and triangular(n)+2 is a prime.
%C Subsequence of A006451 that contains the terms n such that triangular(n)+2 is prime.
%C a(7) is too large to include here (see b-file). - _Max Alekseyev_, Jan 30 2014
%H Max Alekseyev, <a href="/A226071/b226071.txt">Table of n, a(n) for n = 1..12</a>
%t Select[Range[0,220000],IntegerQ[Sqrt[(#(#+1))/2+1]]&&PrimeQ[(#(#+1))/2+2]&] (* _Harvey P. Dale_, Mar 01 2023 *)
%o (C) // see A226069.
%Y Corresponding primes: A226069.
%Y Roots of corresponding squares: A226070.
%Y Cf. A226071-A226074.
%K nonn
%O 1,2
%A _Alex Ratushnyak_, May 25 2013
%E Terms a(7)-a(12) from _Max Alekseyev_, Jan 30 2014