A154113 Primes of the form (n+1)^3 - n^2.

7, 23, 109, 191, 307, 463, 919, 1231, 1607, 2053, 4657, 7639, 8861, 34913, 41719, 53503, 77743, 89189, 95311, 122599, 138007, 146173, 182057, 223381, 246203, 353011, 383833, 416399, 433351, 468623, 505759, 544807, 721079, 745471, 875711

Offset

1,1

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, a[n]]], {n, 6!}]; lst
Select[(#+1)^3-#^2&/@Range[200], PrimeQ]  (* Harvey P. Dale, Mar 14 2011 *)

Prog

(Magma) [a: n in [0..100] | IsPrime(a) where a is (n+1)^3 - n^2]; // Vincenzo Librandi, Sep 02 2016
(PARI) for(n=1, 1e3, if(isprime(t=(n+1)^3 - n^2), print1(t", "))) \\ Charles R Greathouse IV, Sep 02 2016

Crossrefs

Cf. A140719, A005097, A154111, A154112.

Sequence in context: A316734 A096327 A267805 * A340889 A053706 A137367

Adjacent sequences: A154110 A154111 A154112 * A154114 A154115 A154116

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 04 2009

Status

approved