cp's OEIS Frontend

A331166 a(n) = min(n, A057889(n)), where A057889 is bijective base-2 reverse.

%I A331166 #19 Jan 12 2020 23:50:00
%S A331166 0,1,2,3,4,5,6,7,8,9,10,11,12,11,14,15,16,17,18,19,20,21,22,23,24,19,
%T A331166 22,27,28,23,30,31,32,33,34,35,36,37,38,39,40,37,42,43,44,45,46,47,48,
%U A331166 35,38,51,44,43,54,55,56,39,46,55,60,47,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,69,74,83,84,85,86,87,88,77,90,91,92,93,94,95,96,67,70
%N A331166 a(n) = min(n, A057889(n)), where A057889 is bijective base-2 reverse.
%C A331166 There is a large number of sequences b, related to binary expansion of n (A007088), for which it holds that b(n) = b(a(n)) for all n >= 0 (or n >= 1). For example, we have:
%C A331166 For all i, j:
%C A331166   a(i) = a(j) => A002487(i) = A002487(j),
%C A331166   a(i) = a(j) => A005811(i) = A005811(j),
%C A331166   a(i) = a(j) => A286622(i) = A286622(j) => A000120(i) = A000120(j).
%C A331166 For all i, j > 0:
%C A331166   a(i) = a(j) => A007814(i) = A007814(j),
%C A331166   a(i) = a(j) => A280505(i) = A280505(j),
%C A331166   a(i) = a(j) => A305788(i) = A305788(j) => A091222(i) = A091222(j).
%H A331166 Antti Karttunen, <a href="/A331166/b331166.txt">Table of n, a(n) for n = 0..16383</a>
%H A331166 Antti Karttunen, <a href="/A331166/a331166.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A331166 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A331166 a(n) = min(n, A057889(n)).
%o A331166 (PARI)
%o A331166 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A331166 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A331166 A331166(n) = min(n, A057889(n));
%Y A331166 Cf. A000120, A002487, A005811, A007088, A007814, A030101, A057889, A091222, A280505, A286622, A305788.
%Y A331166 Cf. also A330740, A331167, A331173.
%K A331166 nonn,base
%O A331166 0,3
%A A331166 _Antti Karttunen_, Jan 12 2020