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

1,1

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

Links

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

Example

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.

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 &]

Crossrefs

Cf. A001358, A000217, A063637, A063638.

Sequence in context: A261257 A188243 A335104 * A243540 A336384 A124941

Adjacent sequences: A242340 A242341 A242342 * A242344 A242345 A242346

Keyword

nonn

Author

K. D. Bajpai, May 11 2014

Status

approved