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A302028 Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A057889(A057889(n)-1), where A057889 is a bijective bit-reverse.

%I A302028 #9 Dec 23 2024 14:53:45
%S A302028 0,1,2,3,4,5,6,7,8,9,10,13,14,11,12,15,16,17,18,25,26,21,20,29,30,19,
%T A302028 22,23,28,27,24,31,32,33,34,49,50,41,36,57,58,37,38,45,52,53,40,61,62,
%U A302028 35,42,39,54,43,44,47,60,51,46,55,56,59,48,63,64,65,66,97,98,81,68,113,114,73,70,89,100,105,72,121,122,69,74,77,102,85,76
%N A302028 Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A057889(A057889(n)-1), where A057889 is a bijective bit-reverse.
%H A302028 Antti Karttunen, <a href="/A302028/b302028.txt">Table of n, a(n) for n = 0..16383</a>
%H A302028 David Newman, et al., <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2018-January/018239.html">New sequences from old, Discussion on SeqFan-mailing list</a>, January 2018.
%H A302028 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A302028 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A302028 a(0) = 0; for n >= 1, a(n) = 1+A057889(A057889(n)-1).
%o A302028 (PARI)
%o A302028 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A302028 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A302028 A302028(n) = if(!n,n,1+A057889(A057889(n)-1));
%Y A302028 Cf. A302027 (inverse).
%Y A302028 Cf. A057889.
%Y A302028 Cf. also A268718, A302794.
%K A302028 nonn,base
%O A302028 0,3
%A A302028 _Antti Karttunen_, Apr 26 2018