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 A045468 Primes congruent to {1, 4} mod 5. 35
 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491 (list; graph; refs; listen; history; text; internal format)
 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 in A047209, also in A090771. - Reinhard Zumkeller, Jan 07 2012 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 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, Angela Song, Chocolate Numbers, arXiv:1509.06093 [math.CO], 2015. Caleb Ji, Tanya Khovanova, Robin Park, 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 Cf. A000040, A064739, A038872, A010051. Subsequence of A123976. Sequence in context: A158290 A057538 A123976 * A196095 A268271 A053032 Adjacent sequences:  A045465 A045466 A045467 * A045469 A045470 A045471 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 17 18:19 EDT 2018. Contains 316292 sequences. (Running on oeis4.)