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A242343 Triangular numbers T such that (T+2) is semiprime.

%I A242343 #10 Dec 25 2024 17:31:48
%S A242343 36,55,91,120,153,276,300,325,435,595,903,1035,1225,1653,1711,1891,
%T A242343 2016,2145,2485,2556,3003,3240,3741,4095,4465,4560,4851,5253,5460,
%U A242343 5565,5995,6105,6216,6441,6555,6903,7021,7140,7260,8001,8256,8911,9045,9180,9591,10585
%N A242343 Triangular numbers T such that (T+2) is semiprime.
%C A242343 The n-th triangular number T(n) = n*(n+1)/2 = A000217(n).
%C A242343 Triangular numbers of the form p*q - 2, where p and q are primes.
%C A242343 The indices of these triangular numbers are 8, 10, 13, 15, 17, 23, 24, 25, 29, 34, 42, 45, 49, 57, 58, 61, 63, 65, 70, 71, 77, 80, 86, 90, 94, 95, 98, 102, 104, 105, 109, 110, 111, 113, 114, 117, 118, 119, 120, 126, 128, 133, 134, 135, 138, 145, ... - _Wolfdieter Lang_, May 13 2014
%H A242343 K. D. Bajpai, <a href="/A242343/b242343.txt">Table of n, a(n) for n = 1..10000</a>
%e A242343 a(1) = 36 = 8*(8+1)/2 = 36 + 2 = 38 = 2 * 19 is semiprime.
%e A242343 a(2) = 55 = 10*(10+1)/2 = 55 + 2 = 57 = 3 * 19 is semiprime.
%p A242343 with(numtheory): A242343:= proc()local t; t:=x/2*(x+1); if bigomega(t+2)=2 then  RETURN (t); fi;end: seq(A242343 (),x=1..200);
%t A242343 Select[Table[n/2*(n + 1), {n, 200}], PrimeOmega[# + 2] == 2 &]
%t A242343 Select[Accumulate[Range[200]],PrimeOmega[#+2]==2&] (* _Harvey P. Dale_, Dec 25 2024 *)
%Y A242343 Cf.  A001358, A000217, A063637, A063638.
%K A242343 nonn
%O A242343 1,1
%A A242343 _K. D. Bajpai_, May 11 2014