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A336156 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A336158(i) = A336158(j), for all i, j >= 1.

%I A336156 #10 Jul 11 2020 17:58:19
%S A336156 1,2,3,2,4,5,6,2,7,5,3,5,4,5,8,2,4,9,3,5,10,5,6,5,7,5,11,5,4,12,13,2,
%T A336156 10,5,14,9,4,5,15,5,4,12,3,5,16,5,17,5,7,9,14,5,4,18,15,5,10,5,3,12,4,
%U A336156 5,19,2,10,12,3,5,10,12,6,9,4,5,20,5,10,12,17,5,21,5,3,12,10,5,15,5,4,22,14,5,10,5,23,5,4,9,20,9,4,12,6,5,24
%N A336156 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A336158(i) = A336158(j), for all i, j >= 1.
%C A336156 Restricted growth sequence transform of the ordered pair [A007814(1+n), A336158(n)]. Note that A007814(1+n) gives the number of trailing 1-bits in the binary expansion of n.
%C A336156 For all i, j: A324400(i) = A324400(j) => a(i) = a(j).
%H A336156 Antti Karttunen, <a href="/A336156/b336156.txt">Table of n, a(n) for n = 1..65537</a>
%o A336156 (PARI)
%o A336156 up_to = 65537;
%o A336156 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 A336156 A000265(n) = (n>>valuation(n,2));
%o A336156 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336156 A336158(n) = A046523(A000265(n));
%o A336156 A007814(n) = valuation(n,2);
%o A336156 Aux336156(n) = [A007814(1+n), A336158(n)];
%o A336156 v336156 = rgs_transform(vector(up_to, n, Aux336156(n)));
%o A336156 A336156(n) = v336156[n];
%Y A336156 Cf. A000265, A007814, A046523, A336158.
%Y A336156 Cf. also A324400, A336152, A336153, A336154, A336155.
%K A336156 nonn
%O A336156 1,2
%A A336156 _Antti Karttunen_, Jul 11 2020