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A336935 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A278222(i) = A278222(j), for all i, j >= 1.

%I A336935 #5 Aug 10 2020 22:19:58
%S A336935 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,
%T A336935 1,17,9,7,5,18,10,19,3,20,11,21,6,22,12,23,2,24,13,25,7,26,14,27,4,28,
%U A336935 15,29,8,30,16,31,1,32,17,33,9,34,7,35,5,36,18,37,10,38,19,39,3,40,20,41,11,42,21,43,6,44,22,45,12,46,23,47,2,48,24,49,13,50
%N A336935 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A278222(i) = A278222(j), for all i, j >= 1.
%C A336935 Restricted growth sequence transform of the ordered pair [A007733(n), A278222(n)].
%C A336935 For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
%H A336935 Antti Karttunen, <a href="/A336935/b336935.txt">Table of n, a(n) for n = 1..65537</a>
%o A336935 (PARI)
%o A336935 up_to = 65537;
%o A336935 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 A336935 A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
%o A336935 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A336935 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336935 A278222(n) = A046523(A005940(1+n));
%o A336935 Aux336935(n) = [A007733(n), A278222(n)];
%o A336935 v336935 = rgs_transform(vector(up_to, n, Aux336935(n)));
%o A336935 A336935(n) = v336935[n];
%Y A336935 Cf. A000265, A003602, A007733, A278222, A286622, A324400, A336933, A336934.
%K A336935 nonn
%O A336935 1,3
%A A336935 _Antti Karttunen_, Aug 10 2020