A302027 - OEIS

%I #13 Dec 23 2024 14:53:45

%S 0,1,2,3,4,5,6,7,8,9,10,13,14,11,12,15,16,17,18,25,22,21,26,27,30,19,

%T 20,29,28,23,24,31,32,33,34,49,38,41,42,51,46,37,50,53,54,43,58,55,62,

%U 35,36,57,44,45,52,59,60,39,40,61,56,47,48,63,64,65,66,97,70,81,74,99,78,73,82,101,86,83,90,103,94,69,98,105,102,85

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

%H Antti Karttunen, <a href="/A302027/b302027.txt">Table of n, a(n) for n = 0..16383</a>

%H 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 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(0) = 0; for n >= 1, a(n) = A057889(1+A057889(n-1)).

%t f[n_] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]*2^IntegerExponent[n, 2]; Fold[Append[#1, f[1 + f[#2 - 1]]] &, {0, 1}, Range[2, 85]] (* _Michael De Vlieger_, Apr 27 2018, after _Ivan Neretin_ at A057889 *)

%o (PARI)

%o A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));

%o A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));

%o A302027(n) = if(!n,n,A057889(1+A057889(n-1)));

%Y Cf. A302028 (inverse).

%Y Cf. A057889.

%Y Cf. also A268717, A302793.

%K nonn,base,look

%O 0,3

%A _Antti Karttunen_, Apr 26 2018