A272770 Numbers n = concat(s,t) such that n = (Fibonacci(s) mod n) * (Fibonacci(t) mod n).

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

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