

A240884


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


5



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
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OFFSET

1,1


COMMENTS

The nth 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 nth 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



