A164736 Number of n-digit cycles of length 5 under the Kaprekar map A151949.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 5, 0, 6, 0, 6, 1, 6, 3, 6, 5, 6, 6, 6, 6, 7, 6, 9, 6, 11, 6, 12, 6, 12, 7, 12, 9, 12, 11, 12, 12, 12, 12, 13, 12, 15, 12, 17, 12, 18, 12, 18, 13, 18, 15, 18, 17, 18, 18, 18, 18, 19, 18, 21, 18, 23, 18, 24, 18, 24, 19, 24, 21, 24, 23, 24, 24, 24

Offset: 1

Author

Joseph Myers, Aug 23 2009

Keywords

• base
• nonn

Links

• Joseph Myers, Table of n, a(n) for n=1..140
• Index entries for the Kaprekar map

Crossrefs

Cf. A151949, A164727, A164728, A164731, A164732, A164733, A164734, A164735.

Formula

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)

a(n) = a(n-1) + a(n-2) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + a(n-7) + a(n-8) - a(n-9) for n > 15.

G.f.: x^11*(x^2 + 1)*(x^2 - x + 1)/((x - 1)^2*(x + 1)*(x^6 + x^3 + 1)). (End)