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A038807 Future of the smallest-perizeroin komet in Kimberling's expulsion array (A035486).

%I A038807 #24 Feb 16 2025 08:32:38
%S A038807 2,3,5,10,9,20,46,83,12,24,23,36,79,124,172,56,119,61,169,17,42,84,
%T A038807 232,285,596,1186,3190,6857,14225,12495,30482,45827,79090,144112,
%U A038807 423486,1087497,2443796,628733,871389,1199242,2787410,7975876
%N A038807 Future of the smallest-perizeroin komet in Kimberling's expulsion array (A035486).
%C A038807 Could the komet be a planit?
%D A038807 D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.
%D A038807 D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.
%D A038807 Hans Havermann, Algorithm, #4, 1992, p. 2.
%H A038807 Enrique Pérez Herrero, <a href="/A038807/b038807.txt">Table of n, a(n) for n = 0..74</a>
%H A038807 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 A038807 Hans Havermann, <a href="http://chesswanks.com/txt/ARecreationalEndeavour.txt">A Recreational Endeavour</a>
%H A038807 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 A038807 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KimberlingSequence.html">Kimberling Sequence</a>
%F A038807 a(0) = 2; a(n) = a(n-1)-th term in Kimberling's expulsion array (A007063).
%t A038807 K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);
%t A038807 K[i_, j_] := K[i - 1, i - (j + 2)/2] /; (EvenQ[j] && (j < 2 i - 3));
%t A038807 K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));
%t A038807 K[i_] := K[i] = K[i, i]; SetAttributes[K, Listable];
%t A038807 A007063[i_] := K[i];
%t A038807 A038807[1] := 2;
%t A038807 A038807[n_] := A007063[A038807[n - 1]];
%t A038807 ReleaseHold[Table[A038807[n], {n, 1, 35}]]
%t A038807 (* _Enrique Pérez Herrero_, Jan 11 2023 *)
%Y A038807 Cf. A007063, A006852, A038834.
%K A038807 nonn
%O A038807 0,1
%A A038807 _Hans Havermann_