login
A165105
Number of n-digit fixed points under the base-8 Kaprekar map A165090
7
1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 0, 4, 0, 4, 2, 2, 2, 4, 2, 3, 6, 5, 2, 7, 2, 6, 5, 10, 5, 8, 5, 8, 7, 9, 11, 12, 7, 11, 9, 12, 9, 21, 10, 14, 12, 15, 13, 18, 20, 18, 15, 20, 15, 23, 16, 30, 20, 23, 20, 26, 21, 27, 32, 29, 23, 32, 25, 32, 28, 43
OFFSET
1,6
FORMULA
Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = - a(n-1) + a(n-3) + 2*a(n-4) + 2*a(n-5) + a(n-6) - a(n-7) - 2*a(n-8) - 2*a(n-9) - a(n-10) + a(n-12) + a(n-13) for n > 15.
G.f.: x*(-x^14 + x^8 - x^5 + x^4 - x^2 - x - 1)/((x - 1)^3*(x + 1)^2*(x^2 + 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)
CROSSREFS
In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165125 (base 9), A164733 (base 10).
Sequence in context: A247138 A212627 A029419 * A325674 A055641 A218245
KEYWORD
base,nonn
AUTHOR
Joseph Myers, Sep 04 2009
STATUS
approved