A242343 Triangular numbers T such that (T+2) is semiprime.

36, 55, 91, 120, 153, 276, 300, 325, 435, 595, 903, 1035, 1225, 1653, 1711, 1891, 2016, 2145, 2485, 2556, 3003, 3240, 3741, 4095, 4465, 4560, 4851, 5253, 5460, 5565, 5995, 6105, 6216, 6441, 6555, 6903, 7021, 7140, 7260, 8001, 8256, 8911, 9045, 9180, 9591, 10585

Offset: 1

Author

K. D. Bajpai, May 11 2014

Keywords

• nonn

Comments

The n-th triangular number T(n) = n*(n+1)/2 = A000217(n).

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

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

Examples

			a(1) = 36 = 8*(8+1)/2 = 36 + 2 = 38 = 2 * 19 is semiprime.
a(2) = 55 = 10*(10+1)/2 = 55 + 2 = 57 = 3 * 19 is semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A000217, A063637, A063638.

Programs

Maple

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);

Mathematica

Select[Table[n/2*(n + 1), {n, 200}], PrimeOmega[# + 2] == 2 &]
Select[Accumulate[Range[200]],PrimeOmega[#+2]==2&] (* Harvey P. Dale, Dec 25 2024 *)