A240884 - OEIS

%I #11 Aug 25 2014 16:42:03

%S 33,74,237,371,1055,1397,10901,12443,30287,39899,55613,80453,207149,

%T 303041,360467,407999,639797,1230821,1650053,2056511,2695349,2873441,

%U 3454427,3956873,9823349,10384103,13680599,15844877,16419449,20608499,22705373,26508143

%N Semiprimes of the form C(n) + T(n) where C(n) and T(n) are the n-th cube and triangular numbers.

%C The n-th triangular number T(n) = n/2*(n+1).

%C All the terms in the sequence, except a(2), are odd.

%C Semiprimes (biprimes) in the sequence are product of two primes and simultaneously sum of n-th cube & triangular numbers.

%H K. D. Bajpai, <a href="/A240884/b240884.txt">Table of n, a(n) for n = 1..6556</a>

%e a(1) = 33: 3^3 + 3/2*(3+1) = 33 = 3*11, which is product of two primes and hence semiprime.

%e a(3) = 237: 6^3 + 6/2*(6+1) = 237 = 3*79, which is product of two primes and hence semiprime.

%p with(numtheory):KD:= proc() local a,b; a:=(n)^3+n/2*(n+1);b:=bigomega(a); if b=2 then RETURN (a); fi; end: seq(KD(), n=1..500);

%t KD = {}; Do[t = n^3 + n/2*(n + 1); If[PrimeOmega[t] == 2, AppendTo[KD, t]], {n, 500}]; KD

%o (PARI) has(n)=if(n%2, isprime(n) && isprime(n^2+n\2+1), isprime(n/2) && isprime(2*n^2+n+1))

%o for(n=1,1e4, if(has(n), print1(n^3+n*(n+1)/2", "))) \\ _Charles R Greathouse IV_, Aug 25 2014

%Y Cf. A001358, A005898, A046388.

%K nonn,easy

%O 1,1

%A _K. D. Bajpai_, Apr 14 2014