A228908 - OEIS

%I #34 Sep 24 2013 14:49:29

%S 43,421,613,1951,7411,12973,23143,31249,48619,114073,210631,256033,

%T 321403,365509,381061,502441,521641,669901,766039,791431,1015051,

%U 1108693,1242271,1929751,2121793,2773471,3759991,3832999,4057681,5498329,7133281,7472011,7587259

%N Primes of the form T(n) + S(n) + C(n) + 1 where T(n), S(n) and C(n) are the n-th triangular, square and cube numbers.

%C Also primes of the form n^3 + 3/2*n^2 + 1/2*n + 1.

%H K. D. Bajpai, <a href="/A228908/b228908.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 613: T(8)+S(8)+C(8)+1 = 1/2*8*(8+1)+8^2+8^3+1 = 613 which is prime.

%e a(4) = 1951: T(12)+S(12)+C(12)+1 = 1/2*12*(12+1)+12^2+12^3+1 = 1951 which is prime.

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

%o (PARI) select(isprime, vector(100,n,n^3+3/2*n^2+n/2+1)) \\ _Charles R Greathouse IV_, Sep 15 2013

%Y Cf. A120479, A229080.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Sep 14 2013