%I #15 Jul 13 2020 21:32:02
%S 1,2,3,2,4,5,6,2,7,8,9,5,10,11,12,2,13,14,15,8,16,17,18,5,19,20,21,11,
%T 22,23,24,2,25,26,27,14,28,29,30,8,31,32,33,17,34,35,36,5,37,38,39,20,
%U 40,41,42,11,43,44,45,23,46,47,48,2,49,50,51,26,52,53,54,14,55,56,57,29,58,59,60,8,61,62,63,32,64,65,66,17,67,68,69,35,70,71,72,5,73,74,75,38,76,77,78,20,79
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A000265(i) = A000265(j), for all i, j >= 1.
%C Restricted growth sequence transform of the ordered pair [A000035(n), A000265(n)] (parity and the odd part of n), or equally, of the ordered pair [A000265(n), A278221(n)].
%C For all i, j:
%C A324400(i) = A324400(j) => a(i) = a(j),
%C a(i) = a(j) => A336126(i) = A336126(j),
%C a(i) = a(j) => A336147(i) = A336147(j),
%C a(i) = a(j) => A336148(i) = A336148(j),
%C a(i) = a(j) => A336149(i) = A336149(j).
%H Antti Karttunen, <a href="/A336146/b336146.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 A000035(n) = (n%2);
%o A000265(n) = (n>>valuation(n,2));
%o Aux336146(n) = [A000035(n), A000265(n)];
%o v336146 = rgs_transform(vector(up_to, n, Aux336146(n)));
%o A336146(n) = v336146[n];
%Y Cf. A000035, A000265, A046523, A064989, A122111, A278221.
%Y Cf. also A286621, A324400, A336126, A336147, A336148, A336149.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 12 2020