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A345414
a(n) = n^a(n-1) mod 100; a(0) = 0.
1
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
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
KEYWORD
nonn,easy,less
AUTHOR
Joseph Neeley, Jun 18 2021
STATUS
approved