A134198 Number of distinct sequences {i^k mod n; i >= 0} with k >= 0.

1, 2, 3, 4, 5, 3, 7, 5, 8, 5, 11, 4, 13, 7, 5, 8, 17, 8, 19, 6, 7, 11, 23, 5, 22, 13, 21, 8, 29, 5, 31, 13, 11, 17, 13, 8, 37, 19, 13, 7, 41, 7, 43, 12, 14, 23, 47, 8, 44, 22, 17, 14, 53, 21, 21, 9, 19, 29, 59, 6, 61, 31, 8, 22, 13, 11, 67, 18, 23, 13, 71, 9, 73, 37, 22, 20, 31, 13, 79, 8

Offset

1,2

Links

David W. Wilson, Table of n, a(n) for n = 1..10000

Formula

a(n) = A051903(n) + A002322(n).

Example

Let S(k) be the sequence (0^k, 1^k, 2^k, ...) mod 8. S(k) is periodic with period 8 and we find that (1,1,1,1,1,1,1,1,...) = S(0), (0,1,2,3,4,5,6,7,...) = S(1), (0,1,4,1,0,1,4,1,...) = S(2), (0,1,0,3,0,5,0,7,...) = S(3) = S(5) = S(7) = ... and (0,1,0,1,0,1,0,1,...) = S(4) = S(6) = S(8) = ... The first A002322(8) = 3 sequences occur for exactly one value of k. The remaining A051903(8) = 2 sequences occur for an infinite number of k. This gives a(8) = 3+2 = 5.

Crossrefs

Sequence in context: A346088 A275823 A141295 * A060653 A274690 A081810

Adjacent sequences: A134195 A134196 A134197 * A134199 A134200 A134201

Keyword

nonn

Author

David W. Wilson, Oct 13 2007

Status

approved