A164725 -id:A164725 - cp's OEIS frontend

A164723 Numbers belonging to cycles of length 2 under the Kaprekar map A151949.

53955, 59994, 8733209876622, 9665429654331, 873332098766622, 966543296654331, 8764421997755322, 8765431997654322, 87333320987666622, 96654332966654331, 8733333209876666622, 9665433329666654331

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..1146
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164725, A164727, A164729, A164724.

A164726 Least element of each cycle of length 3 under the Kaprekar map A151949.

Original entry on oeis.org

64308654, 6431088654, 6433086654, 6543086544, 9751088421, 643110888654, 643310886654, 643330866654, 654310886544, 654330866544, 655430865444, 975110888421, 975310886421, 975510884421, 997510884201, 64311108888654

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..9283
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A164718, A164720, A164724, A164728, A164730, A164725.

A164727 Numbers belonging to cycles of length 5 under the Kaprekar map A151949.

Original entry on oeis.org

86420987532, 86541975432, 87641975322, 88431976512, 96641975331, 8643209876532, 8654209875432, 8654319765432, 8764209875322, 8764319765322, 8765419754322, 8843209876512, 8843319766512, 8854319765412, 8874319765212

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..14510
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164723, A164725, A164729, A164728.

A164735 Number of n-digit cycles of length 3 under the Kaprekar map A151949.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 10, 0, 20, 0, 36, 0, 60, 1, 94, 4, 141, 10, 204, 21, 286, 39, 392, 66, 527, 105, 696, 159, 906, 231, 1164, 326, 1477, 449, 1854, 605, 2304, 801, 2836, 1044, 3462, 1341, 4194, 1701, 5044, 2133, 6027, 2646, 7158, 3252, 8452, 3963

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n = 1..70
M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023. [see page 45]
M. Kauers and C. Koutschan, Conjectured closed form for a(n), a quasi-polynomial of period 18 and degree 5.
Index entries for the Kaprekar map

Cf. A151949, A164725, A164726, A164731, A164732, A164733, A164734, A164736.

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = 4*a(n-2) - 6*a(n-4) + 5*a(n-6) - 5*a(n-8) + a(n-9) + 6*a(n-10) - 4*a(n-11) - 4*a(n-12) + 6*a(n-13) + a(n-14) - 5*a(n-15) + 5*a(n-17) - 6*a(n-19) + 4*a(n-21) - a(n-23) for n > 25.
G.f.: x*(-x^24 + x^22 + x^18 - x^16 + x^15 - x^13 + x^7)/((x - 1)^6*(x + 1)^5*(x^2 - x + 1)*(x^2 + x + 1)^2*(x^6 + x^3 + 1)). (End)

A164729 Numbers belonging to cycles of length 7 under the Kaprekar map A151949.

Original entry on oeis.org

420876, 642654, 750843, 840852, 851742, 860832, 862632, 43208766, 64326654, 75308643, 84308652, 85317642, 86308632, 86326632, 4332087666, 6433266654, 7533086643, 8433086652, 8533176642, 8633086632, 8633266632, 433320876666

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..476
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164723, A164725, A164727, A164730.

cp's OEIS Frontend

A164723 Numbers belonging to cycles of length 2 under the Kaprekar map A151949.

Views

Author

Keywords

Links

Crossrefs

A164726 Least element of each cycle of length 3 under the Kaprekar map A151949.

Views

Author

Keywords

Links

Crossrefs

A164727 Numbers belonging to cycles of length 5 under the Kaprekar map A151949.

Views

Author

Keywords

Links

Crossrefs

A164735 Number of n-digit cycles of length 3 under the Kaprekar map A151949.

Views

Author

Keywords

Links

Crossrefs

Formula

A164729 Numbers belonging to cycles of length 7 under the Kaprekar map A151949.

Views

Author

Keywords

Links

Crossrefs