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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
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
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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, May 11 2014
STATUS
approved