|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy,less
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|