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%I #7 Jul 11 2020 17:58:11
%S 1,2,3,2,4,2,5,2,1,6,7,2,8,6,9,2,10,2,11,6,4,12,13,2,10,14,3,6,15,6,
%T 16,2,17,18,19,2,20,21,22,6,15,6,23,12,4,24,25,2,10,18,19,14,26,2,27,
%U 6,28,29,30,6,31,12,32,2,33,12,34,18,35,18,36,2,37,38,19,21,28,14,39,6,1,29,40,6,41,42,43,12,44,6,45,24,17,46,47,2,48,18,7,18,49,18,50,14,10
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A335915(i) = A335915(j), for all i, j >= 1.
%C Restricted growth sequence transform of the ordered pair [A007814(1+n), A335915(n)]. Note that A007814(1+n) gives the number of trailing 1-bits in the binary expansion of n.
%C For all i, j: A324400(i) = A324400(j) => a(i) = a(j).
%H Antti Karttunen, <a href="/A336155/b336155.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o 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 A007814(n) = valuation(n,2);
%o A000265(n) = (n>>valuation(n,2));
%o A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1)*A000265(f[k,1]+1))^f[k,2])); };
%o Aux336155(n) = [A007814(1+n), A335915(n)];
%o v336155 = rgs_transform(vector(up_to, n, Aux336155(n)));
%o A336155(n) = v336155[n];
%Y Cf. A000265, A007814, A335915.
%Y Cf. also A324400, A336154, A336156, A336162.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 11 2020
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