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A242356 Triangular numbers T such that both (T+2) and (T-2) are semiprimes. 1

%I

%S 36,120,276,300,325,903,1653,2485,2556,3240,4851,5253,5460,5995,6105,

%T 6441,6903,8001,8256,8911,9591,10585,12561,12720,14365,20301,21115,

%U 22791,23436,24753,26335,26565,26796,27495,29161,30381,31375,34191,34980,37401,40755

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

%C The n-th triangular number T(n) = n*(n+1)/2.

%C Triangular numbers of the form p*q - 2 and r*s + 2 where p, q, r and s are primes.

%H K. D. Bajpai, <a href="/A242356/b242356.txt">Table of n, a(n) for n = 1..6565</a>

%e a(1) = 36 = 8*(8+1)/2 = 36 + 2 = 38 = 2 * 19 and 36 - 2 = 34 = 2 * 17 both are semiprimes.

%e a(2) = 120 = 15*(15+1)/2 = 120 + 2 = 122 = 2 * 61 and 120 - 2 = 118 = 2 * 59 both are semiprimes.

%p 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 Select[Table[n*(n + 1)/2, {n, 500}], PrimeOmega[# + 2] == 2 && PrimeOmega[# - 2] == 2 &]

%t Select[Accumulate[Range[300]],PrimeOmega[#+{2,-2}]=={2,2}&] (* _Harvey P. Dale_, Apr 21 2016 *)

%Y Cf. A001358, A000217, A063637, A063638.

%K nonn

%O 1,1

%A _K. D. Bajpai_, May 11 2014

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Last modified June 20 09:30 EDT 2021. Contains 345162 sequences. (Running on oeis4.)