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Future of the smallest-perizeroin komet in Kimberling's expulsion array (A035486).
6

%I #23 Jan 12 2023 20:37:07

%S 2,3,5,10,9,20,46,83,12,24,23,36,79,124,172,56,119,61,169,17,42,84,

%T 232,285,596,1186,3190,6857,14225,12495,30482,45827,79090,144112,

%U 423486,1087497,2443796,628733,871389,1199242,2787410,7975876

%N Future of the smallest-perizeroin komet in Kimberling's expulsion array (A035486).

%C Could the komet be a planit?

%D D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.

%D D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.

%D Hans Havermann, Algorithm, #4, 1992, p. 2.

%H Enrique Pérez Herrero, <a href="/A038807/b038807.txt">Table of n, a(n) for n = 0..74</a>

%H Lars Blomberg & Hans Havermann, <a href="https://spreadsheets.google.com/ccc?key=0Ars3II3ElHF_dHN4aVhseV90WDJSSTlJQXJQVzl5cGc&amp;hl=en">komets & planits (250 kometary path fragments)</a>

%H Hans Havermann, <a href="http://chesswanks.com/txt/ARecreationalEndeavour.txt">A Recreational Endeavour</a>

%H Clark Kimberling, <a href="https://cms.math.ca/crux/backfile/Crux_v17n02_Feb.pdf">Problem 1615</a>, Crux Mathematicorum, Vol. 17 (2) 44 1991; <a href="https://cms.math.ca/crux/backfile/Crux_v18n03_Mar.pdf">Solution to Problem 1615</a>, Crux Mathematicorum, Vol. 18, March 1992, pp. 82-83.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KimberlingSequence.html">Kimberling Sequence</a>

%F a(0) = 2; a(n) = a(n-1)-th term in Kimberling's expulsion array (A007063).

%t K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);

%t K[i_, j_] := K[i - 1, i - (j + 2)/2] /; (EvenQ[j] && (j < 2 i - 3));

%t K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));

%t K[i_] := K[i] = K[i, i]; SetAttributes[K, Listable];

%t A007063[i_] := K[i];

%t A038807[1] := 2;

%t A038807[n_] := A007063[A038807[n - 1]];

%t ReleaseHold[Table[A038807[n], {n, 1, 35}]]

%t (* _Enrique Pérez Herrero_, Jan 11 2023 *)

%Y Cf. A007063, A006852, A038834.

%K nonn

%O 0,1

%A _Hans Havermann_