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

1,1

Comments

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

Links

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

Example

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.

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);

Prog

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

Crossrefs

Cf. A120479, A229080.

Sequence in context: A142770 A142841 A142913 * A027002 A093673 A244769

Adjacent sequences: A228905 A228906 A228907 * A228909 A228910 A228911

Keyword

nonn

Author

K. D. Bajpai, Sep 14 2013

Status

approved