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

36, 120, 276, 300, 325, 903, 1653, 2485, 2556, 3240, 4851, 5253, 5460, 5995, 6105, 6441, 6903, 8001, 8256, 8911, 9591, 10585, 12561, 12720, 14365, 20301, 21115, 22791, 23436, 24753, 26335, 26565, 26796, 27495, 29161, 30381, 31375, 34191, 34980, 37401, 40755

Offset: 1

Author

K. D. Bajpai, May 11 2014

Keywords

• nonn

Comments

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

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

Examples

			a(1) = 36 = 8*(8+1)/2 = 36 + 2 = 38 = 2 * 19 and  36 - 2 = 34 = 2 * 17 both are semiprimes.
a(2) = 120 = 15*(15+1)/2 = 120 + 2 = 122 = 2 * 61 and 120 - 2 = 118 = 2 * 59 both are semiprimes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..6565

Crossrefs

Cf. A001358, A000217, A063637, A063638.

Programs

Maple

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);

Mathematica

Select[Table[n*(n + 1)/2, {n, 500}], PrimeOmega[# + 2] == 2 && PrimeOmega[# - 2] == 2 &]
Select[Accumulate[Range[300]],PrimeOmega[#+{2,-2}]=={2,2}&] (* Harvey P. Dale, Apr 21 2016 *)