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A042993 Primes congruent to {0, 2, 3} mod 5. 11
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)