A154112 Numbers k such that (k+1)^3 - k^2 is prime.

1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 16, 19, 20, 32, 34, 37, 42, 44, 45, 49, 51, 52, 56, 60, 62, 70, 72, 74, 75, 77, 79, 81, 89, 90, 95, 96, 97, 100, 101, 104, 105, 111, 114, 115, 121, 126, 131, 136, 145, 151, 154, 156, 161, 171, 174, 175, 180, 182, 191, 199, 200, 202, 207

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 04 2009

Keywords

• nonn
• easy

Examples

			2^3-1^2 = 7, 3^3-2^2 = 23, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A140719, A005097, A154111.

Programs

Magma

[n: n in [0..5000] | IsPrime(((n+1)^3-n^2))]; // Vincenzo Librandi, Nov 26 2010

Mathematica

a[n_]:=(n+1)^3-n^2;lst={};Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,6!}];lst
Select[Range[210],PrimeQ[(#+1)^3-#^2]&] (* Harvey P. Dale, Sep 20 2011 *)

PARI

is(n)=isprime((n+1)^3 - n^2) \\ Charles R Greathouse IV, Sep 02 2016