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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 1 14:52 EST 2022. Contains 358468 sequences. (Running on oeis4.)