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%I #8 May 13 2014 18:29:02
%S 36,55,91,120,153,276,300,325,435,595,903,1035,1225,1653,1711,1891,
%T 2016,2145,2485,2556,3003,3240,3741,4095,4465,4560,4851,5253,5460,
%U 5565,5995,6105,6216,6441,6555,6903,7021,7140,7260,8001,8256,8911,9045,9180,9591,10585
%N Triangular numbers T such that (T+2) is semiprime.
%C The n-th triangular number T(n) = n*(n+1)/2 = A000217(n).
%C Triangular numbers of the form p*q - 2, where p and q are primes.
%C 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 K. D. Bajpai, <a href="/A242343/b242343.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 36 = 8*(8+1)/2 = 36 + 2 = 38 = 2 * 19 is semiprime.
%e a(2) = 55 = 10*(10+1)/2 = 55 + 2 = 57 = 3 * 19 is semiprime.
%p 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 Select[Table[n/2*(n + 1), {n, 200}], PrimeOmega[# + 2] == 2 &]
%Y Cf. A001358, A000217, A063637, A063638.
%K nonn
%O 1,1
%A _K. D. Bajpai_, May 11 2014
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