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A272770 Numbers n = concat(s,t) such that n = (Fibonacci(s) mod n) * (Fibonacci(t) mod n). 1
2105, 3648, 3770, 4875, 22205, 34205, 36480, 37750, 42375, 58105, 64512, 78805, 79300, 82805, 88805, 99005, 102205, 128105, 147905, 172805, 194105, 196205, 230105, 236105, 280205, 284105, 299905, 300288, 313750, 316805, 357120, 364800, 370944, 378624, 383905, 396205 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

Fibonacci(21) mod 2105 * Fibonacci(5) mod 2105 = 10946 mod 2105 * 5 mod 2105 = 421 * 5 = 2105;

Fibonacci(222) mod 22205 * Fibonacci(5) mod 22205= 11111460156937785151929026842503960837766832936 mod 22205 * 5 mod 22205 = 4441 * 5= 22205.

MAPLE

with(combinat): P:=proc(q) local a, b, i, n;

for n from 1 to q do for i from 1 to ilog10(n) do

a:=trunc(n/10^i);  b:=n-a*10^i; if b>0 then

if (fibonacci(a) mod n)*(fibonacci(b) mod n)=n then print(n); break;

fi; fi; od;  od; end: P(10^9);

MATHEMATICA

Select[Range[10^5], Total@ Boole@ Function[k, k == Mod[Fibonacci@ First@ #, k] Mod[Fibonacci@ Last@ #, k] & /@ Map[FromDigits /@ TakeDrop[IntegerDigits@ k, #] &, Range[IntegerLength@ k - 1]]]@ # > 0 &] (* Michael De Vlieger, May 07 2016, Version 10.2 *)

CROSSREFS

Cf. A000045, A272767.

Sequence in context: A015293 A159812 A233729 * A284962 A146895 A300008

Adjacent sequences:  A272767 A272768 A272769 * A272771 A272772 A272773

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, May 06 2016

STATUS

approved

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Last modified October 16 03:52 EDT 2021. Contains 348035 sequences. (Running on oeis4.)