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A045468
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Primes congruent to {1, 4} mod 5.
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45
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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
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OFFSET
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1,1
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COMMENTS
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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
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
Appears to be the primes p such that p^6 mod 210 = 1. - Gary Detlefs, Dec 29 2011
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
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REFERENCES
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Hardy and Wright, An Introduction to the Theory of Numbers, Chap. X, p. 150, Oxford University Press, Fifth edition.
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LINKS
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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.
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MAPLE
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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
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MATHEMATICA
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Select[Prime[Range[200]], MemberQ[{1, 4}, Mod[#, 5]]&] (* Vincenzo Librandi, Aug 13 2012 *)
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PROG
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(Haskell)
a045468 n = a045468_list !! (n-1)
a045468_list = [x | x <- a047209_list, a010051 x == 1]
(Magma) [ p: p in PrimesUpTo(1000) | p mod 5 in {1, 4} ]; // Vincenzo Librandi, Aug 13 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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