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

1,2

Links

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

Example

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

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 *)

Prog

(Magma) [n: n in [0..5000] | IsPrime(((n+1)^3-n^2))]; // Vincenzo Librandi, Nov 26 2010
(PARI) is(n)=isprime((n+1)^3 - n^2) \\ Charles R Greathouse IV, Sep 02 2016

Crossrefs

Cf. A140719, A005097, A154111.

Sequence in context: A024616 A023733 A380699 * A039101 A140102 A376956

Adjacent sequences: A154109 A154110 A154111 * A154113 A154114 A154115

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 04 2009

Status

approved