cp's OEIS Frontend

A057030 Let P(n) of a sequence s(1),s(2),s(3),... be obtained by leaving s(1),...,s(n-1) fixed and reversing 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 A057030.

%I A057030 #19 Apr 24 2024 07:52:41
%S A057030 1,3,4,6,11,13,14,22,27,29,40,42,47,55,66,68,83,85,86,110,115,123,138,
%T A057030 140,161,179,180,182,223,231,236,270,275,277,314,332,337,371,382,384,
%U A057030 425,427,438,472,477,537,542,550,555,619,630
%N A057030 Let P(n) of a sequence s(1),s(2),s(3),... be obtained by leaving s(1),...,s(n-1) fixed and reversing 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 A057030.
%H A057030 Peter J. C. Moses, <a href="/A057030/b057030.txt">Table of n, a(n) for n = 1..5000</a>
%F A057030 Conjecture: a(n) = A007062(n+1) - 1 for n > 0. - _Mikhail Kurkov_, Mar 10 2022
%e A057030 PS(2) begins with 1,3,2,5,4,7,6;
%e A057030 PS(3) begins with 1,3,4,5,2,9,6;
%e A057030 PS(4) begins with 1,3,4,6,9,2,5.
%t A057030 a057030=Range[x=3500]; Do[a057030=Flatten[Join[{Take[a057030,n-1]},Map[Reverse,Partition[Drop[a057030,n-1],n]]]],{n,2,NestWhile[#+1&,1,(x=# Floor[x/#])>0&]-1}]; a057030 (* _Peter J. C. Moses_, Nov 10 2016 *)
%Y A057030 Cf. A007062, A057032, A057033, A057063, A057064.
%K A057030 nonn,nice,easy
%O A057030 1,2
%A A057030 _Clark Kimberling_, Jul 29 2000