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A001583 Artiads: the primes p == 1 mod 5 for which Fibonacci((p-1)/5) is divisible by p.
(Formerly M5413 N2351)
18
211, 281, 421, 461, 521, 691, 881, 991, 1031, 1151, 1511, 1601, 1871, 1951, 2221, 2591, 3001, 3251, 3571, 3851, 4021, 4391, 4441, 4481, 4621, 4651, 4691, 4751, 4871, 5081, 5281, 5381, 5531, 5591, 5641, 5801, 5881, 6011, 6101, 6211, 6271, 6491, 6841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

L. Tanner, Proc. London Math. Soc., 18 (1886-1887), 214-234; 24 (1892-1893), 223-262.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..24903, Apr 01, 2016 [First 1000 terms from T. D. Noe]

E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131.

E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131 [annotated and corrected scanned copy]

E. Lehmer, On the quadratic character of the Fibonacci root, Fib. Quart., 4 (1966), 135-138 (annotated scanned copy).

MAPLE

with(combinat): P:= proc(n) local p; p:=ithprime(n);

if p mod 5=1 and type(fibonacci((p-1)/5)/p, integer) then p; fi; end:

seq(P(i), i=1..10^4); # Paolo P. Lava, May 10 2017

MATHEMATICA

Select[ Prime[ Range[1000]], Mod[#, 5] == 1 && Divisible[ Fibonacci[(# - 1)/5], #] &] (* Jean-Fran├žois Alcover, Jun 22 2012 *)

PROG

(Haskell)

a001583 n = a001583_list !! (n-1)

a001583_list = filter

   (\p -> mod (a000045 $ div (p - 1) 5) p == 0) a030430_list

-- Reinhard Zumkeller, Aug 15 2013

(PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]

list(lim)=my(v=List()); forprime(p=11, lim, if(p%5==1 && fibmod(p\5, p)==0, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 06 2017

CROSSREFS

Cf. A047650, A000045, A024894, subsequence of A030430.

See also A270798 (a subsequence), A270800.

Sequence in context: A087833 A240918 A096706 * A137870 A137871 A142582

Adjacent sequences:  A001580 A001581 A001582 * A001584 A001585 A001586

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Jan 25 2000

Edited by N. J. A. Sloane, Apr 01 2016

STATUS

approved

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Last modified November 17 19:40 EST 2017. Contains 294834 sequences.