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A023164 Numbers k such that Fib(k) == -3 (mod k). 1
1, 2, 8, 68, 92, 188, 212, 332, 428, 452, 548, 668, 692, 788, 908, 932, 1028, 1052, 1172, 1268, 1292, 1388, 1412, 1508, 1532, 1772, 1868, 2012, 2074, 2156, 2228, 2252, 2314, 2348, 2372, 2468, 2588, 2612, 2708, 2732, 2972, 3092, 3188, 3308, 3428, 3452, 3548 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Includes 4*p for primes p with p == 17 or 23 (mod 30). - Robert Israel, May 11 2021

LINKS

Robert Israel, Table of n, a(n) for n = 1..2000

MAPLE

fpp:= n -> mpow(n-1, n)[2, 2]:

M:= <<0, 1>|<1, 1>>:

mpow:= proc(n, p)

  if n = 0 then <<1, 0>|<0, 1>>

  elif n::even then procname(n/2, p)^2 mod p

  else  procname((n-1)/2, p)^2 . M mod p

  fi

end proc:

select(t -> fpp(t)+3 mod t = 0, [$1..10000]); # Robert Israel, May 11 2021

MATHEMATICA

Select[Range[3600], Mod[Fibonacci[#]+3, #]==0&] (* Harvey P. Dale, Sep 21 2021 *)

CROSSREFS

Cf. A002708

Sequence in context: A132219 A226730 A202553 * A053922 A030445 A093990

Adjacent sequences:  A023161 A023162 A023163 * A023165 A023166 A023167

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Definition clarified by N. J. A. Sloane, Sep 21 2021

STATUS

approved

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Last modified October 18 19:31 EDT 2021. Contains 348069 sequences. (Running on oeis4.)