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 A242356 Triangular numbers T such that both (T+2) and (T-2) are semiprimes. 1
 36, 120, 276, 300, 325, 903, 1653, 2485, 2556, 3240, 4851, 5253, 5460, 5995, 6105, 6441, 6903, 8001, 8256, 8911, 9591, 10585, 12561, 12720, 14365, 20301, 21115, 22791, 23436, 24753, 26335, 26565, 26796, 27495, 29161, 30381, 31375, 34191, 34980, 37401, 40755 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The n-th triangular number T(n) = n*(n+1)/2. Triangular numbers of the form p*q - 2 and r*s + 2 where p, q, r and s are primes. LINKS K. D. Bajpai, Table of n, a(n) for n = 1..6565 EXAMPLE a(1) = 36 = 8*(8+1)/2 = 36 + 2 = 38 = 2 * 19 and  36 - 2 = 34 = 2 * 17 both are semiprimes. a(2) = 120 = 15*(15+1)/2 = 120 + 2 = 122 = 2 * 61 and 120 - 2 = 118 = 2 * 59 both are semiprimes. MAPLE with(numtheory): A242356:= proc()local t; t:=x*(x+1)/2; if bigomega(t+2)=2 and bigomega(t-2)=2 then  RETURN (t); fi; end: seq(A242356 (), x=1..500); MATHEMATICA Select[Table[n*(n + 1)/2, {n, 500}], PrimeOmega[# + 2] == 2 && PrimeOmega[# - 2] == 2 &] Select[Accumulate[Range[300]], PrimeOmega[#+{2, -2}]=={2, 2}&] (* Harvey P. Dale, Apr 21 2016 *) CROSSREFS Cf. A001358, A000217, A063637, A063638. Sequence in context: A044668 A129367 A287861 * A165966 A307939 A254146 Adjacent sequences:  A242353 A242354 A242355 * A242357 A242358 A242359 KEYWORD nonn AUTHOR K. D. Bajpai, May 11 2014 STATUS approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)