A359143 The sum-and-erase sequence starting at 11: a(0) = 11; for n>=1, let m = a(n-1), and if m < 0, change m to an improper decimal "number" by replacing the minus sign by a single leading zero; then a(n) = A359142(m).
11, 112, 1124, 11248, 2486, 4860, 486018, 48601827, 4860182736, 8601827365, 860182736546, 86018273654656, 8601827365465667, 601273654656670, -1273545704, -127354570438, -12735457043849, -1273545704384962, 1273545743849627, 127354574384962777, 273545743849627779
Offset: 0
Links
- Eric Angelini, Does this iteration end? (Sum and erase), Personal blog "Cinquante Signes", blogspot.com, Jul 26 2022.
- Eric Angelini, Does this iteration end? (Sum and erase), Personal blog "Cinquante Signes", blogspot.com, Jul 26 2022. [Cached copy, pdf file, with permission]
- Michael S. Branicky, Python program for the sum-and-erase sequence
- Jean-Paul Delahaye, Des suites à la dynamique insaisissable, Pour la Science #549, July 2023, pp. 80-85. (Link requires a subscription.)
- Hans Havermann, Table of n, a(n) for n = 0..1399141 [Beware, this is a 106.5 MB file.]
- Hans Havermann, Cycles in Éric Angelini's sum-and-erase, Glad Hobo Express Blog, Jul 28 2022
- Hans Havermann, A cycle of length 49 [Astonishing! - _N. J. A. Sloane_, Jan 31 2023]
- N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)
Programs
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Mathematica
a[1] = {1, 1}; nn = 21; Do[If[FreeQ[#3, #2], Set[k, #1~Join~#3], Set[k, #1~Join~#3]; Set[k, DeleteCases[#1~Join~#3, #2]]] & @@ {#, First[#], IntegerDigits@ Total[#]} &[a[n - 1]]; Set[a[n], k], {n, 2, nn}]; Array[(1 - 2 Boole[First[#] == 0])*FromDigits@ # &@ a[#] &, nn] (* Michael De Vlieger, Mar 16 2023 *)
Comments