A042993 - OEIS

A042993

Primes congruent to {0, 2, 3} mod 5.

2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 127, 137, 157, 163, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 433, 443, 457

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OFFSET

1,1

COMMENTS

Also, primes p that are quadratic nonresidues modulo 5 (and from the quadratic reciprocity law, odd p such that 5 is a quadratic nonresidue modulo p). For primes p' that are quadratic residues modulo 5 (and such that 5 is a quadratic residue mod p') see A045468. - Lekraj Beedassy, Jul 13 2004

Primes p that divide Fibonacci(p+1). - Ron Knott, Jun 27 2014

REFERENCES

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, Theorem 180

LINKS

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

EXAMPLE

For prime 7, Fibonacci(8) = 21 = 3*7, for prime 13, Fibonacci(14) = 377 = 13*29.

MATHEMATICA

Select[Prime[Range[100]], MemberQ[{0, 2, 3}, Mod[#, 5]]&] (* Harvey P. Dale, Mar 03 2012 *)

PROG

(Magma) [p: p in PrimesUpTo(600) | p mod 5 in [0, 2, 3]]; // Vincenzo Librandi, Aug 09 2012

CROSSREFS

Primes dividing A001654.

Cf. A038872 for primes p which divide Fibonacci(p-1). - Ron Knott, Jun 27 2014

Sequence in context: A262839 A234695 A067905 * A308711 A033664 A024785

Adjacent sequences: A042990 A042991 A042992 * A042994 A042995 A042996

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved