OFFSET
1,3
COMMENTS
a(n) = (5^(5^(5^(5^(5^ ... ))))) mod n, provided sufficient 5s are in the tower such that adding more doesn't affect the value of a(n).
LINKS
Wayne VanWeerthuizen, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 5^a(A000010(n)) mod n. For n<=18, a(n)=(5^5) mod n.
EXAMPLE
a(2) = 1, as 5^X is odd for any whole number X.
a(19) = 6, as 5^(5^5) == 5^(5^(5^5)) == 5^(5^(5^(5^5))) == 6 (mod 19).
MAPLE
A:= proc(n) option remember; 5 &^ A(numtheory:-phi(n)) mod n end proc:
A(2):= 1;
seq(A(n), n=2..100);
MATHEMATICA
a[n_] := a[n] = PowerMod[5, If[n <= 18, 5, a[EulerPhi[n]]], n];
Array[a, 100] (* Jean-François Alcover, Jul 25 2022 *)
PROG
(Sage)
def a(n):
if ( n <= 18 ):
return 3125%n
else:
return power_mod(5, a(euler_phi(n)), n)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wayne VanWeerthuizen, Aug 08 2014
STATUS
approved