A227412 Primes of the form n^3 + (n+1)^3 + 2.

11, 37, 191, 857, 2333, 3061, 4943, 6121, 9011, 22817, 33203, 89533, 105527, 114193, 341993, 421381, 536771, 931087, 1005041, 1294561, 1386443, 1583047, 1911493, 2416061, 4866481, 5086811, 5199427, 5429621, 7376141, 7814207, 8903071, 9399097, 9739811, 9913213

Offset: 1

Author

K. D. Bajpai, Sep 22 2013

Keywords

• nonn

Comments

Primes which are sum of two consecutive cubes plus 2.

Examples

			a(2)=37: k^3+(k+1)^3+2= 2^3+3^3+2= 8+27+2= 37 which is prime.
a(3)=191: k^3+(k+1)^3+2= 4^3+5^3+2= 64+125+2= 191 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A027862, A227340.

Programs

Maple

KD:= proc() local a; a:= (k)^3+(k+1)^3+2; if isprime(a) then RETURN(a): fi;end: seq(KD(),k=1..500);

Mathematica

Select[Table[(x^3+(x+1)^3+2), {x, 1000}], PrimeQ]

Formula

Primes of the form 2*n^3 + 3*n^2 + 3*n + 3.