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

0,1

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

Formula

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

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 *)

Crossrefs

Cf. A007063, A006852, A038834.

Sequence in context: A244489 A367297 A286144 * A094542 A175481 A288244

Adjacent sequences: A038804 A038805 A038806 * A038808 A038809 A038810

Keyword

nonn

Author

Hans Havermann

Status

approved