A240884 Semiprimes of the form C(n) + T(n) where C(n) and T(n) are the n-th cube and triangular numbers.

33, 74, 237, 371, 1055, 1397, 10901, 12443, 30287, 39899, 55613, 80453, 207149, 303041, 360467, 407999, 639797, 1230821, 1650053, 2056511, 2695349, 2873441, 3454427, 3956873, 9823349, 10384103, 13680599, 15844877, 16419449, 20608499, 22705373, 26508143

Offset

1,1

Comments

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

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

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

Links

K. D. Bajpai, Table of n, a(n) for n = 1..6556

Example

a(1) = 33: 3^3 + 3/2*(3+1) = 33 = 3*11, which is product of two primes and hence semiprime.
a(3) = 237: 6^3 + 6/2*(6+1) = 237 = 3*79, which is product of two primes and hence semiprime.

Maple

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);

Mathematica

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

Prog

(PARI) has(n)=if(n%2, isprime(n) && isprime(n^2+n\2+1), isprime(n/2) && isprime(2*n^2+n+1))
for(n=1, 1e4, if(has(n), print1(n^3+n*(n+1)/2", "))) \\ Charles R Greathouse IV, Aug 25 2014

Crossrefs

Cf. A001358, A005898, A046388.

Sequence in context: A103046 A063868 A184417 * A049012 A137187 A354916

Adjacent sequences: A240881 A240882 A240883 * A240885 A240886 A240887

Keyword

nonn,easy

Author

K. D. Bajpai, Apr 14 2014

Status

approved