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A336936 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A007733(n), A329697(n), A331410(n)], for all i, j >= 1.

%I A336936 #5 Aug 11 2020 10:38:44
%S A336936 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,10,4,14,8,15,
%T A336936 1,16,9,17,5,18,10,17,3,19,11,20,6,21,12,22,2,23,13,24,7,25,10,26,4,
%U A336936 27,14,28,8,29,15,30,1,21,16,31,9,32,17,33,5,34,18,35,10,36,17,37,3,38,19,39,11,40,20,41,6,42,21,43,12,44,22,45,2,46,23,47,13
%N A336936 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A007733(n), A329697(n), A331410(n)], for all i, j >= 1.
%C A336936 Restricted growth sequence transform of the triplet [A007733(n), A329697(n), A331410(n)], or equally, of the ordered pair [A007733(n), A335880(n)].
%C A336936 For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
%H A336936 Antti Karttunen, <a href="/A336936/b336936.txt">Table of n, a(n) for n = 1..65537</a>
%o A336936 (PARI)
%o A336936 up_to = 65537;
%o A336936 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 A336936 A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
%o A336936 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A336936 A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
%o A336936 Aux336936(n) = [A007733(n), A329697(n), A331410(n)];
%o A336936 v336936 = rgs_transform(vector(up_to, n, Aux336936(n)));
%o A336936 A336936(n) = v336936[n];
%Y A336936 Cf. A003602, A007733, A329697, A331410, A335880.
%Y A336936 Cf. also A324400, A336920, A336933, A336934, A336935.
%K A336936 nonn
%O A336936 1,3
%A A336936 _Antti Karttunen_, Aug 11 2020