OFFSET
1,1
COMMENTS
Rational primes that decompose in the field Q(sqrt(5)). - N. J. A. Sloane, Dec 26 2017
These are also primes p that divide Fibonacci(p-1). - Jud McCranie
Primes ending in 1 or 9. - Lekraj Beedassy, Oct 27 2003
Also primes p such that p divides 5^(p-1)/2 - 4^(p-1)/2. - Cino Hilliard, Sep 06 2004
Primes p such that the polynomial x^2-x-1 mod p has 2 distinct zeros. - T. D. Noe, May 02 2005
Same as A038872, apart from the term 5. - R. J. Mathar, Oct 18 2008
Appears to be the primes p such that p^6 mod 210 = 1. - Gary Detlefs, Dec 29 2011
Primes p such that p does not divide Sum_{i=1..p} Fibonacci(i)^2. The sum is A001654(p). - Arkadiusz Wesolowski, Jul 23 2012
Primes congruent to {1, 9} mod 10. Legendre symbol (5, a(n)) = +1. For prime 5 this symbol (5, 5) is set to 0, and (5, prime) = -1 for prime == {3, 7} (mod 10), given in A003631. - Wolfdieter Lang, Mar 05 2021
REFERENCES
Hardy and Wright, An Introduction to the Theory of Numbers, Chap. X, p. 150, Oxford University Press, Fifth edition.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Caleb Ji, Tanya Khovanova, Robin Park, and Angela Song, Chocolate Numbers, arXiv:1509.06093 [math.CO], 2015.
Caleb Ji, Tanya Khovanova, Robin Park, and Angela Song, Chocolate Numbers, Journal of Integer Sequences, Vol. 19 (2016), #16.1.7.
MAPLE
for n from 1 to 500 do if(isprime(n)) and (n^6 mod 210=1) then print(n) fi od; # Gary Detlefs, Dec 29 2011
MATHEMATICA
lst={}; Do[p=Prime[n]; If[Mod[p, 5]==1||Mod[p, 5]==4, AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
Select[Prime[Range[200]], MemberQ[{1, 4}, Mod[#, 5]]&] (* Vincenzo Librandi, Aug 13 2012 *)
PROG
(PARI) list(lim)=select(n->n%5==1||n%5==4, primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011
(Haskell)
a045468 n = a045468_list !! (n-1)
a045468_list = [x | x <- a047209_list, a010051 x == 1]
-- Reinhard Zumkeller, Jan 07 2012
(Magma) [ p: p in PrimesUpTo(1000) | p mod 5 in {1, 4} ]; // Vincenzo Librandi, Aug 13 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved