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A229157 Primes of the form T(n) + C(n) - 1 where T(n) and C(n) are n-th triangular and cube numbers.

%I A229157 #9 Sep 24 2013 14:48:03
%S A229157 73,139,547,773,2287,4231,8209,9491,36497,111767,118873,177211,217829,
%T A229157 316777,391717,596273,889391,1005049,1035451,1163189,1265597,1301023,
%U A229157 1449337,1735259,2105407,2524771,3319123,4755827,5467351,6246523,6348829,6662437,8636239,9151273
%N A229157 Primes of the form T(n) + C(n) - 1 where T(n) and C(n) are n-th triangular and cube numbers.
%C A229157 Also primes of the form (2*n^3 + n^2 + n - 2)/2.
%H A229157 K. D. Bajpai, <a href="/A229157/b229157.txt">Table of n, a(n) for n = 1..5000</a>
%e A229157 a(3)=547: T(8)+C(8)-1 = (1/2)*8*(8+1)+8^3-1 = 547 which is prime.
%e A229157 a(4)=773: T(9)+C(9)-1 = (1/2)*9*(9+1)+9^3-1 = 773 which is prime.
%p A229157 KD:= proc() local a,b,d; a:= (1/2)*n*(n+1);b:=n^3; d:=a+b-1; if isprime(d) then   RETURN(d): fi;end:seq(KD(),n=1..500);
%Y A229157 Cf. A120479, A229080.
%K A229157 nonn
%O A229157 1,1
%A A229157 _K. D. Bajpai_, Sep 15 2013