cp's OEIS Frontend

A057033 Let P(n) of a sequence s(1),s(2),s(3),... be obtained by leaving s(1),...s(n-1) fixed and reverse-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) is A057033.

%I A057033 #23 Apr 24 2024 07:54:40
%S A057033 1,3,5,2,9,11,6,15,17,10,21,12,4,27,29,18,19,35,22,39,41,8,45,28,30,
%T A057033 51,36,34,57,59,14,43,65,42,69,71,24,53,77,7,81,60,54,87,64,58,67,95,
%U A057033 26,99,101,37,105,107,70,111,84,32,88,93,78,47
%N A057033 Let P(n) of a sequence s(1),s(2),s(3),... be obtained by leaving s(1),...s(n-1) fixed and reverse-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) is A057033.
%F A057033 Conjecture: a(n) = A057063(n+1) - 1 for n > 0. - _Mikhail Kurkov_, Mar 08 2023
%e A057033 PS(2) begins with 1,3,2,5,4,7,6; PS(3) with 1,3,5,4,2,6,9; PS(4) with 1,3,5,2,6,9,4.
%t A057033 terms = 62; maxTerms = terms^2; Clear[PS]; PS[n_] := PS[n] = If[n == 1, Range[maxTerms], Join[PS[n-1][[1 ;; n-1]], RotateLeft /@ Partition[ PS[n-1][[n ;; All]], n]] // Flatten]; PS[1]; PS[n = 2]; While[PS[n][[1 ;; terms]] != PS[n-1][[1 ;; terms]], n++]; A057033 = PS[n][[1 ;; terms]] (* _Jean-François Alcover_, Apr 24 2017 *)
%Y A057033 Cf. A007062, A057030, A057032, A057063, A057064, A069836.
%K A057033 nonn,nice,easy
%O A057033 1,2
%A A057033 _Clark Kimberling_, Jul 29 2000