cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Tomas Rokicki

Tomas Rokicki's wiki page.

Tomas Rokicki has authored 3 sequences.

A372008 Maximum number of moves to solve "Reverse The List of Integers" game with high value n.

Original entry on oeis.org

0, 0, 0, 0, 0, 14, 26, 74, 86, 126, 106, 130
Offset: 1

Author

Tomas Rokicki, Apr 15 2024

Keywords

Comments

Given a list of unique positive integers with a maximum value n, you can perform the following "moves": a) split one number into two numbers that sum to the original number, or b) add two adjacent numbers into a new number. In all moves the list must not have duplicates or contain a value greater than n.
Some lists can be reversed (e.g., 1,6,3) and some cannot (e.g., 1,6,4). The "distance" of a list is the smallest number of a moves to reverse it; this sequence deals with the maximum distance of all reversible lists.
For n<6, the only lists that can be reversed are the ones that are single-number sequences that are implicitly reversed in 0 moves.

Examples

			For n=6, the worst case is 1,6,3 -> 1,4,2,3 -> 5,2,3 -> 4,1,2,3 -> 4,1,5 -> 4,6 -> 1,3,6 -> 1,3,2,4 -> 1,5,4 -> 6,4 -> 5,1,4 -> 3,2,1,4 -> 3,2,5 -> 3,2,4,1 -> 3,6,1.  There is no shorter solution for this list, and no other reversible list requires more than 14 moves. So a(6) = 14.
		

A308721 Locations of the first occurrence of pair (0,n) in the van Eck sequence (A181391).

Original entry on oeis.org

0, 1, 3, 20, 24, 10, 30, 276, 388, 81, 225, 726, 2935, 1408, 7718, 5624, 5680, 85998, 26706, 546290, 1112929, 702575, 3425417, 10537360, 21301906, 217230900, 108698091, 32381774, 846522986, 851764846, 11692311325, 46163898987
Offset: 0

Author

Tomas Rokicki, Jun 19 2019

Keywords

Comments

a(33) = 118456929919 and a(34) = 250327022558 but we do not yet know a(32).

Examples

			For a(5)=10, the pair (0,5) first occurs in A181391 at element 10.
		

Crossrefs

Cf. A181391.

Programs

  • Mathematica
    With[{s = Nest[# /. {{Longest[p___], a_, q___, a_} :> {p, a, q, a, Length[{a, q}]}, {a___} :> {a, 0}} &, {}, 10^3]}, TakeWhile[#, # > -1 &] &@ Array[If[Length@ # == 0, -1, #[[1, 1]] - 1 ] &@ SequencePosition[s, {0, #}] &, Max@ s, 0]] (* Michael De Vlieger, Jul 08 2019, after JungHwan Min at A181391 *)

A317188 a(n) = 1 + 2 * (a(n-1) + a(n-4) + a(n-6)) + a(n-7) for n>3, with initial values 0 if n<0, and 1,3,8,18 for n=0..3.

Original entry on oeis.org

1, 3, 8, 18, 39, 85, 189, 422, 942, 2099, 4673, 10400, 23148, 51528, 114709, 255359, 568460, 1265450, 2817015, 6270953, 13959773, 31075874, 69178058, 153997383, 342813793, 763138256, 1698823128, 3781752544, 8418564665, 18740578667, 41718428560, 92869452514
Offset: 0

Author

Tomas Rokicki, Jul 28 2018

Keywords

Comments

Some mail programs automatically include copies of all earlier messages in the same thread. In some cases (especially when rich text format is used) any unrecognized character is replaced by two copies of itself, leading to exponential growth.
The present sequence illustrates this growth for UTF-8 encoding and the CP1252 character set, for the single code point 150.

References

  • Fred Lunnon and Tomas Rokicki, Posting to Math Fun Mailing List, circa Jul 25 2018

Programs

  • Mathematica
    LinearRecurrence[{3,-2,0,2,-2,2,-1,-1},{1,3,8,18,39,85,189,422},40] (* Harvey P. Dale, Oct 15 2021 *)

Formula

G.f.: -(x^4-x^2-1)/((x-1)*(x+1)*(x^6+x^5-x^4+3*x^3-3*x^2+3*x-1)). - Alois P. Heinz, Jul 28 2018

Extensions

More terms from Altug Alkan, Jul 28 2018