%I #11 May 10 2016 00:41:35
%S 153,168,233,267,459,538,557,637,642,684,699,1169,1178,1183,1206,1224,
%T 1278,1334,1368,2052,2142,2161,2221,2391,2448,2814,2838,2862,4284,
%U 4836,4896,5050,5292,5535,5631,5814,5845,5901,5915,6426,7182,7866,7883,8052,8208,8346
%N Numbers n = concat(s,t) such that n = (Fibonacci(s) mod n) + (Fibonacci(t) mod n).
%H Paolo P. Lava, <a href="/A272767/b272767.txt">Table of n, a(n) for n = 1..500</a>
%e Fibonacci(15) mod 153 + Fibonacci(3) mod 153 = 610 mod 153 + 2 mod 153 = 151 + 2 = 153;
%e Fibonacci(23) mod 2391 + Fibonacci(91) mod 2391 = 28657 mod 2391 + 4660046610375530309 mod 2391 = 2356 + 35 = 2391;
%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[10^4], 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, A272770.
%K nonn,easy,base
%O 1,1
%A _Paolo P. Lava_, May 06 2016