A345414 a(n) = n^a(n-1) mod 100; a(0) = 0.

0, 1, 2, 9, 44, 25, 76, 1, 8, 21, 0, 1, 12, 81, 64, 25, 76, 81, 68, 41, 0, 1, 22, 29, 24, 25, 76, 61, 28, 61, 0, 1, 32, 61, 84, 25, 76, 41, 88, 81, 0, 1, 42, 49, 4, 25, 76, 21, 48, 1, 50, 1, 52, 41, 4, 25, 76, 1, 58, 21, 0, 1, 62, 69, 84, 25, 76, 81, 68, 41, 0, 1

Offset

0,3

Comments

a(n+100) = a(n).

0 <= a(n) <= 94 for all integers n.

a(10*k) = 0.

a(n+1) = 1 and a(n+2) = n mod 100 iff a(n)=0.

Limit_{n->oo} (1/n)*Sum_{j=1..n} a(j) = 38.3.

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Example

a(2) = 2^1 mod 100 = 2 mod 100 = 2;
a(3) = 3^2 mod 100 = 9 mod 100 = 9;
a(4) = 4^9 mod 100 = 262144 mod 100 = 44;
a(5) = 5^44 mod 100 = 5684341886080801486968994140625 mod 100 = 25.

Mathematica

a[n_] := Mod[n^a[n - 1], 100]; a[0] = 0; Array[a, 72, 0] (* Robert G. Wilson v, Nov 14 2023 *)

Crossrefs

Sequence in context: A324619 A292099 A020113 * A272199 A260074 A294270

Adjacent sequences: A345411 A345412 A345413 * A345415 A345416 A345417

Keyword

nonn,easy,less

Author

Joseph Neeley, Jun 18 2021

Status

approved