A164726 -id:A164726 - cp's OEIS frontend

A164724 Least element of each cycle of length 2 under the Kaprekar map A151949.

53955, 8733209876622, 873332098766622, 8764421997755322, 87333320987666622, 8733333209876666622, 873333332098766666622, 87333333320987666666622, 87764442219997775553222, 8733333333209876666666622

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..573
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A164718, A164720, A164726, A164728, A164730, A164723.

A164725 Numbers belonging to cycles of length 3 under the Kaprekar map A151949.

Original entry on oeis.org

64308654, 83208762, 86526432, 6431088654, 6433086654, 6543086544, 8321088762, 8332087662, 8653266432, 8655264432, 8732087622, 8765264322, 9751088421, 9755084421, 9775084221, 643110888654, 643310886654, 643330866654

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..27849
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A099010, A164716, A164723, A164727, A164729, A164726.

A164728 Least element of each cycle of length 5 under the Kaprekar map A151949.

Original entry on oeis.org

86420987532, 8643209876532, 8654209875432, 8764209875322, 864332098766532, 865432098765432, 876432098765322, 876542098754322, 885432098765412, 86433320987666532, 86543320987665432, 87643320987665322

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..2902
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A164718, A164720, A164724, A164726, A164730, A164727.

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)

A164730 Least element of each cycle of length 7 under the Kaprekar map A151949.

Original entry on oeis.org

420876, 43208766, 4332087666, 433320876666, 43333208766666, 4333332087666666, 433333320876666666, 43333333208766666666, 4333333332087666666666, 433333333320876666666666

Offset: 1

Joseph Myers, Aug 23 2009

Joseph Myers, Table of n, a(n) for n=1..68
Index entries for the Kaprekar map

Cf. A151949, A151959, A099009, A164718, A164720, A164724, A164726, A164728, A164729.

cp's OEIS Frontend

A164724 Least element of each cycle of length 2 under the Kaprekar map A151949.

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A164725 Numbers belonging to cycles of length 3 under the Kaprekar map A151949.

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A164728 Least element of each cycle of length 5 under the Kaprekar map A151949.

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

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A164730 Least element of each cycle of length 7 under the Kaprekar map A151949.

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