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A242356 Triangular numbers T such that both (T+2) and (T-2) are semiprimes.

%I A242356 #12 Apr 21 2016 12:22:30
%S A242356 36,120,276,300,325,903,1653,2485,2556,3240,4851,5253,5460,5995,6105,
%T A242356 6441,6903,8001,8256,8911,9591,10585,12561,12720,14365,20301,21115,
%U A242356 22791,23436,24753,26335,26565,26796,27495,29161,30381,31375,34191,34980,37401,40755
%N A242356 Triangular numbers T such that both (T+2) and (T-2) are semiprimes.
%C A242356 The n-th triangular number T(n) = n*(n+1)/2.
%C A242356 Triangular numbers of the form p*q - 2 and r*s + 2 where p, q, r and s are primes.
%H A242356 K. D. Bajpai, <a href="/A242356/b242356.txt">Table of n, a(n) for n = 1..6565</a>
%e A242356 a(1) = 36 = 8*(8+1)/2 = 36 + 2 = 38 = 2 * 19 and  36 - 2 = 34 = 2 * 17 both are semiprimes.
%e A242356 a(2) = 120 = 15*(15+1)/2 = 120 + 2 = 122 = 2 * 61 and 120 - 2 = 118 = 2 * 59 both are semiprimes.
%p A242356 with(numtheory): A242356:= proc()local t; t:=x*(x+1)/2; if bigomega(t+2)=2 and bigomega(t-2)=2 then  RETURN (t); fi;end: seq(A242356 (),x=1..500);
%t A242356 Select[Table[n*(n + 1)/2, {n, 500}], PrimeOmega[# + 2] == 2 && PrimeOmega[# - 2] == 2 &]
%t A242356 Select[Accumulate[Range[300]],PrimeOmega[#+{2,-2}]=={2,2}&] (* _Harvey P. Dale_, Apr 21 2016 *)
%Y A242356 Cf. A001358, A000217, A063637, A063638.
%K A242356 nonn
%O A242356 1,1
%A A242356 _K. D. Bajpai_, May 11 2014