A057032 Let P(n) of a sequence s(1), s(2), s(3), ... be obtained by leaving s(1), ..., s(n-1) fixed and forward-cyclically permuting every n consecutive terms thereafter; apply P(2) to 1, 2, 3, ... to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) as n -> oo is this sequence.

1, 3, 4, 7, 6, 10, 8, 16, 15, 21, 12, 22, 14, 27, 28, 36, 18, 33, 20, 43, 35, 39, 24, 53, 34, 45, 46, 50, 30, 66, 32, 78, 52, 57, 55, 81, 38, 63, 59, 88, 42, 86, 44, 96, 87, 75, 48, 119, 64, 111, 76, 101, 54, 103, 79, 144, 83, 93, 60, 141, 62, 99, 113, 173, 91, 136, 68, 139

Offset

1,2

Comments

Conjecture: a(n) - 1 is prime if and only if a(n) = n + 1. - Mikhail Kurkov, Mar 10 2022

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

Conjecture: a(n) = A057064(n+1) - 1 for n > 0. - Mikhail Kurkov, Mar 10 2022

Example

PS(2) begins with 1, 3, 2, 5, 4, 7, 6;
PS(3) begins with 1, 3, 4, 2, 5, 9, 7;
PS(4) begins with 1, 3, 4, 7, 2, 5, 9.

Mathematica

PS[i_, n_] := If[i == 1, n, If[n < i, PS[i-1, n], If[Mod[n, i] == 0, PS[i-1, n+i-1], PS[i-1, n-1]]]]; a[n_] := PS[n, n]; Table[a[n], {n, 1, 68}] (* Jean-François Alcover, Oct 20 2011, after MATLAB *)

Prog

(MATLAB) function m = A057032(i) m = PS(i, i); function m = PS(i, n) if i == 1 m = n; elseif n < i m = PS(i - 1, n); else if mod(n, i) == 0 m = PS(i - 1, n + i - 1); else m = PS(i - 1, n - 1); end end
(PARI) a(n) = { my (p=0); forstep (d=n, 1, -1, if (p%d==0, p+=d)); p } \\ Rémy Sigrist, Aug 25 2020

Crossrefs

Cf. A007062, A057030, A057033, A057063, A057064, A069829.

Sequence in context: A175187 A332993 A126253 * A347529 A279388 A292288

Adjacent sequences: A057029 A057030 A057031 * A057033 A057034 A057035

Keyword

nonn,nice,easy

Author

Clark Kimberling, Jul 29 2000

Extensions

More terms from David Wasserman, Apr 22 2002

Status

approved