A272770 - OEIS

%I #10 May 10 2016 00:41:52

%S 2105,3648,3770,4875,22205,34205,36480,37750,42375,58105,64512,78805,

%T 79300,82805,88805,99005,102205,128105,147905,172805,194105,196205,

%U 230105,236105,280205,284105,299905,300288,313750,316805,357120,364800,370944,378624,383905,396205

%N Numbers n = concat(s,t) such that n = (Fibonacci(s) mod n) * (Fibonacci(t) mod n).

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

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

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

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

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

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

%p fi; fi; od;  od; end: P(10^9);

%t 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 *)

%Y Cf. A000045, A272767.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, May 06 2016