A111223 Numbers n such that 5*n + 2 is prime.

0, 1, 3, 7, 9, 13, 19, 21, 25, 27, 31, 33, 39, 45, 51, 55, 61, 63, 67, 69, 73, 79, 91, 93, 97, 109, 111, 115, 117, 121, 123, 129, 135, 145, 151, 157, 159, 165, 171, 175, 177, 181, 187, 189, 193, 195, 199, 217, 219, 223, 237, 243, 247, 255, 259, 261, 265, 273, 285

Offset

1,3

References

T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley, New York, 2001, p. 410 (Theorem 34.8).

Links

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

Formula

a(n) = F(p-2)/5 mod p, where p is the n-th prime number such that p==2 (mod 5) and F(m) is m-th Fibonacci number. - Rigoberto Florez, Mar 02 2020

Example

97 is in the sequence because 5*97 + 2 = 487 is prime.

Mathematica

Select[Range[0, 1000], PrimeQ[5 # + 2] &] (* Vincenzo Librandi, May 20 2014 *)
Table[If[PrimeQ[5p+2], Mod[5^(-1) Fibonacci[5p], 5p+2],  Unevaluated[Sequence[]]], {p, 0, 250}] (* Rigoberto Florez, Mar 02 2020 *)
Select[(#-2)/5&/@Prime[Range[250]], IntegerQ] (* Harvey P. Dale, Sep 27 2023 *)

Prog

(Magma) [n: n in [0..350] | IsPrime(5*n+2)]; // Vincenzo Librandi, Nov 13 2010
(PARI) is(n)=isprime(5*n+2) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A024894.

Sequence in context: A032375 A089556 A225495 * A266836 A066207 A141544

Adjacent sequences: A111220 A111221 A111222 * A111224 A111225 A111226

Keyword

nonn,easy

Author

Parthasarathy Nambi, Oct 26 2005

Status

approved