

A242343


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


2



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
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OFFSET

1,1


COMMENTS

The nth 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



