A100662 Primes of the form k^3 + (k+1)^2.

5, 17, 43, 89, 593, 829, 2393, 2969, 3631, 5237, 11177, 12743, 14449, 16301, 27961, 33857, 40529, 44171, 56393, 60919, 75937, 93241, 127601, 198593, 219721, 266369, 278981, 499439, 578843, 621521, 689393, 737281, 787337, 839609, 950993, 980299, 1010201, 1071817

Offset: 1

Author

Giovanni Teofilatto, Jan 03 2005

Keywords

• nonn
• easy

Examples

			a(1) = 5 because 5 = 1^3 + 2^2.
a(2) = 17 because 17 = 2^3 + 3^2.
a(3) = 43 because 43 = 3^3 + 4^2.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A100705 and A000040.

Cf. A127483.

Programs

Magma

[ a: n in [0..100] | IsPrime(a) where a is n^3 + (n+1)^2 ]; // Vincenzo Librandi, Jul 18 2012

Mathematica

Select[Table[n^3+(n+1)^2,{n,200}],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)

PARI

list(lim)=my(v=List(),t); for(n=1,lim, t=n^3+(n+1)^2; if(t>lim, break); if(isprime(t), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Dec 23 2016

Formula

a(n) = A100705(A127483(n)). - Elmo R. Oliveira, Apr 19 2025

Extensions

More terms from Mark Hudson, Jan 04 2005