OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 2241 terms from Klaus Brockhaus)
FORMULA
EXAMPLE
Fibonacci(12) = 144, 144 mod 12 = 0, and 0 is a Fibonacci number. Therefore 12 is in the sequence.
Fibonacci(14) = 377, 377 mod 14 = 13, and 13 is a Fibonacci number. Therefore 14 is in the sequence.
MAPLE
isA000045 := proc(n) local F, i; for i from 0 do F := combinat[fibonacci](i) ; if F> n then return false; elif F = n then return true; end if; end do; end proc:
isA182625 := proc(n) isA000045(combinat[fibonacci](n) mod n) ; end proc:
for n from 1 to 300 do if isA182625(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Apr 02 2011
# second Maple program:
b:= proc(n) local r, M, p; r, M, p:=
<<1|0>, <0|1>>, <<0|1>, <1|1>>, n;
do if irem(p, 2, 'p')=1 then r:= r.M mod n fi;
if p=0 then break fi; M:= M.M mod n
od; r[1, 2]
end:
a:= proc(n) option remember; local k;
for k from 1+`if`(n=1, 0, a(n-1)) while (t->
not (issqr(t+4) or issqr(t-4)))(5*b(k)^2)
do od; k
end:
seq(a(n), n=1..100); # Alois P. Heinz, Nov 26 2016
MATHEMATICA
nn=12; f=Table[Fibonacci[n], {n, 0, nn}]; Select[Range[f[[-1]]], MemberQ[f, Mod[Fibonacci[#], #]]&] (* T. D. Noe, Apr 02 2011 *)
PROG
(PARI) is(n)=my(k=(fibonacci(n)%n)^2); k+=(k+1)<<2; issquare(k) || issquare(k-8) \\ Charles R Greathouse IV, Jul 30 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Carmine Suriano, Mar 30 2011
STATUS
approved