A228908 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.

43, 421, 613, 1951, 7411, 12973, 23143, 31249, 48619, 114073, 210631, 256033, 321403, 365509, 381061, 502441, 521641, 669901, 766039, 791431, 1015051, 1108693, 1242271, 1929751, 2121793, 2773471, 3759991, 3832999, 4057681, 5498329, 7133281, 7472011, 7587259

Offset: 1

Author

K. D. Bajpai, Sep 14 2013

Keywords

• nonn

Comments

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

Examples

			a(3) = 613: T(8)+S(8)+C(8)+1 = 1/2*8*(8+1)+8^2+8^3+1 = 613 which is prime.
a(4) = 1951: T(12)+S(12)+C(12)+1 = 1/2*12*(12+1)+12^2+12^3+1 = 1951 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A120479, A229080.

Programs

Maple

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);

PARI

select(isprime, vector(100,n,n^3+3/2*n^2+n/2+1)) \\ Charles R Greathouse IV, Sep 15 2013