A090693 Positive numbers n such that n^2 - 2n + 2 is a prime.

2, 3, 5, 7, 11, 15, 17, 21, 25, 27, 37, 41, 55, 57, 67, 75, 85, 91, 95, 111, 117, 121, 125, 127, 131, 135, 147, 151, 157, 161, 171, 177, 181, 185, 205, 207, 211, 225, 231, 237, 241, 251, 257, 261, 265, 271, 281, 285, 301, 307, 315, 327, 341, 351, 385, 387, 397

Offset: 1

Author

Giovanni Teofilatto, Dec 19 2003

Keywords

• easy
• nonn

References

• M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
• Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Crossrefs

A002496 gives primes, A062325 gives prime index. Cf. A001912.

A005574(n+1) + 1.

Programs

Mathematica

a={};Do[If[PrimeQ[n^2-2n+2],AppendTo[a,n]],{n,1000}];a (* Peter J. C. Moses, Apr 02 2013 *)
Select[Range[400],PrimeQ[#^2-2#+2]&] (* Harvey P. Dale, May 10 2013 *)

Python

# Python 3.2 or higher required.
from itertools import accumulate
from sympy import isprime
A090693_list = [i for i,n in enumerate(accumulate(range(10**5),lambda x,y:x+2*y-3)) if i > 0 and isprime(n+2)] # Chai Wah Wu, Sep 23 2014

Formula

a(n) = A005574(n)+1.

Extensions

Corrected and extended by Ray Chandler, Dec 28 2003

Definition corrected by Chai Wah Wu, Sep 23 2014