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A245972 Tower of 5s mod n. 9

%I

%S 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,

%T 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,

%U 44,9,48,5,14,25,38,53,5,23,5,65,5,45,1,29,34,35,50

%N Tower of 5s mod n.

%C 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).

%H Wayne VanWeerthuizen, <a href="/A245972/b245972.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 5^a(A000010(n)) mod n. For n<=18, a(n)=(5^5) mod n.

%e a(2) = 1, as 5^X is odd for any whole number X.

%e a(19) = 6, as 5^(5^5) == 5^(5^(5^5)) == 5^(5^(5^(5^5))) == 6 (mod 19).

%p A:= proc(n) option remember; 5 &^ A(numtheory:-phi(n)) mod n end proc:

%p A(2):= 1;

%p seq(A(n), n=2..100);

%o (Sage)

%o def a(n):

%o if ( n <= 18 ):

%o return 3125%n

%o else:

%o return power_mod(5,a(euler_phi(n)),n)

%Y Cf. A240162, A245970, A245971, A245973, A245974.

%K nonn,easy

%O 1,3

%A _Wayne VanWeerthuizen_, Aug 08 2014

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Last modified September 28 21:22 EDT 2021. Contains 347717 sequences. (Running on oeis4.)