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

2, 3, 5, 10, 9, 20, 46, 83, 12, 24, 23, 36, 79, 124, 172, 56, 119, 61, 169, 17, 42, 84, 232, 285, 596, 1186, 3190, 6857, 14225, 12495, 30482, 45827, 79090, 144112, 423486, 1087497, 2443796, 628733, 871389, 1199242, 2787410, 7975876

Offset: 0

Author

Hans Havermann

Keywords

• nonn

Comments

Could the komet be a planit?

References

• D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.
• D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.
• Hans Havermann, Algorithm, #4, 1992, p. 2.

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 0..74
• Lars Blomberg & Hans Havermann, komets & planits (250 kometary path fragments)
• Hans Havermann, A Recreational Endeavour
• Clark Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991; Solution to Problem 1615, Crux Mathematicorum, Vol. 18, March 1992, pp. 82-83.
• Eric Weisstein's World of Mathematics, Kimberling Sequence

Crossrefs

Cf. A007063, A006852, A038834.

Programs

Mathematica

K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);
K[i_, j_] := K[i - 1, i - (j + 2)/2] /; (EvenQ[j] && (j < 2 i - 3));
K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));
K[i_] := K[i] = K[i, i]; SetAttributes[K, Listable];
A007063[i_] := K[i];
A038807[1] := 2;
A038807[n_] := A007063[A038807[n - 1]];
ReleaseHold[Table[A038807[n], {n, 1, 35}]]
(* Enrique Pérez Herrero, Jan 11 2023 *)

Formula

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