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A324346 Lexicographically earliest positive sequence such that a(i) = a(j) => A005811(i) = A005811(j) and A324055(i) = A324055(j), for all i, j >= 0.

%I A324346 #7 Feb 24 2019 17:52:39
%S A324346 1,2,3,2,4,5,6,2,7,8,9,10,11,12,13,2,14,15,16,17,18,19,20,21,22,23,24,
%T A324346 25,26,21,22,2,27,28,29,5,30,19,18,31,32,33,34,35,36,37,38,39,40,41,
%U A324346 42,43,44,45,46,47,48,49,50,51,52,53,54,2,55,56,18,15,57,19,58,59,60,61,62,63,64,65,32,66,67,68,69,63,70,71,72,73,74,75,76,77,78,79,80,81
%N A324346 Lexicographically earliest positive sequence such that a(i) = a(j) => A005811(i) = A005811(j) and A324055(i) = A324055(j), for all i, j >= 0.
%C A324346 Restricted growth sequence transform of the ordered pair [A005811(n), A324055(n)].
%H A324346 Antti Karttunen, <a href="/A324346/b324346.txt">Table of n, a(n) for n = 0..65537</a>
%H A324346 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A324346 For all n >= 1, a((2^n)-1) = 2.
%o A324346 (PARI)
%o A324346 up_to = 65537;
%o A324346 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 A324346 A005811(n) = hammingweight(bitxor(n, n>>1)); \\ From A005811
%o A324346 A324055(n) = { my(m1=2,m2=1,p=2,mp=p*p); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, m1 *= p; if(3==(n%4),mp *= p,m2 *= (mp-1)/(p-1))); n>>=1); (m1-m2); };
%o A324346 Aux324346(n) = [A005811(n), A324055(n)];
%o A324346 v324346 = rgs_transform(vector(1+up_to,n,Aux324346(n-1)));
%o A324346 A324346(n) = v324346[1+n];
%Y A324346 Cf. A005811, A324055, A324345, A324347.
%K A324346 nonn
%O A324346 0,2
%A A324346 _Antti Karttunen_, Feb 24 2019