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A324530 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A033879(n), A318458(n)] for all other numbers, except f(1) = -1.

%I A324530 #7 Mar 05 2019 18:20:02
%S A324530 1,2,3,2,4,5,6,2,7,8,9,10,11,12,13,2,14,15,16,17,9,18,19,20,21,22,23,
%T A324530 24,25,26,27,2,16,28,19,29,30,31,19,32,33,34,35,36,37,38,39,40,41,42,
%U A324530 43,44,45,46,47,48,49,50,51,52,53,54,55,2,39,56,57,58,35,59,60,61,62,63,64,65,51,66,67,68,41,69,70,71,72,73,74,75,76,77,78,79,51,80
%N A324530 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A033879(n), A318458(n)] for all other numbers, except f(1) = -1.
%H A324530 Antti Karttunen, <a href="/A324530/b324530.txt">Table of n, a(n) for n = 1..65537</a>
%H A324530 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324530 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324530 a(2^n) = 2 for all n >= 1.
%o A324530 (PARI)
%o A324530 up_to = 65537;
%o A324530 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A324530 A033879(n) = (n+n-sigma(n));
%o A324530 A318458(n) = bitand(n,sigma(n)-n);
%o A324530 Aux324530(n) = if(1==n,-1,[A033879(n), A318458(n)]);
%o A324530 v324530 = rgs_transform(vector(up_to,n,Aux324530(n)));
%o A324530 A324530(n) = v324530[n];
%Y A324530 Cf. A033879, A318458, A324389, A324400, A324531.
%K A324530 nonn
%O A324530 1,2
%A A324530 _Antti Karttunen_, Mar 05 2019