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A272767
Numbers n = concat(s,t) such that n = (Fibonacci(s) mod n) + (Fibonacci(t) mod n).
2
153, 168, 233, 267, 459, 538, 557, 637, 642, 684, 699, 1169, 1178, 1183, 1206, 1224, 1278, 1334, 1368, 2052, 2142, 2161, 2221, 2391, 2448, 2814, 2838, 2862, 4284, 4836, 4896, 5050, 5292, 5535, 5631, 5814, 5845, 5901, 5915, 6426, 7182, 7866, 7883, 8052, 8208, 8346
OFFSET
1,1
LINKS
EXAMPLE
Fibonacci(15) mod 153 + Fibonacci(3) mod 153 = 610 mod 153 + 2 mod 153 = 151 + 2 = 153;
Fibonacci(23) mod 2391 + Fibonacci(91) mod 2391 = 28657 mod 2391 + 4660046610375530309 mod 2391 = 2356 + 35 = 2391;
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[10^4], 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 *)
CROSSREFS
Sequence in context: A183985 A184045 A203603 * A104810 A352222 A253023
KEYWORD
nonn,easy,base
AUTHOR
Paolo P. Lava, May 06 2016
STATUS
approved