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A245972
Tower of 5s mod n.
9
0, 1, 2, 1, 0, 5, 3, 5, 2, 5, 1, 5, 5, 3, 5, 5, 14, 11, 6, 5, 17, 1, 5, 5, 0, 5, 2, 17, 9, 5, 25, 21, 23, 31, 10, 29, 35, 25, 5, 5, 9, 17, 28, 1, 20, 5, 23, 5, 45, 25, 14, 5, 51, 29, 45, 45, 44, 9, 48, 5, 14, 25, 38, 53, 5, 23, 5, 65, 5, 45, 1, 29, 34, 35, 50
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
STATUS
approved