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

1,1

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001358, A000217, A063637, A063638.

Sequence in context: A129367 A350500 A287861 * A165966 A307939 A254146

Adjacent sequences: A242353 A242354 A242355 * A242357 A242358 A242359

Keyword

nonn

Author

K. D. Bajpai, May 11 2014

Status

approved