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A364950 Lexicographically earliest infinite sequence such that a(i) = a(j) => A025480(i) = A025480(j) and A348717(i) = A348717(j) for all i, j >= 1.

%I A364950 #10 Aug 17 2023 19:26:06
%S A364950 1,2,3,4,2,5,3,6,4,7,2,8,9,10,11,12,13,14,15,16,7,17,2,18,19,20,21,22,
%T A364950 23,24,3,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,2,40,41,42,43,
%U A364950 44,45,46,47,48,49,50,23,51,52,53,54,55,56,57,58,59,60,61,13,62,63,64,14,65,66,67,15,68,69,70,34,71
%N A364950 Lexicographically earliest infinite sequence such that a(i) = a(j) => A025480(i) = A025480(j) and A348717(i) = A348717(j) for all i, j >= 1.
%C A364950 Restricted growth sequence transform of the ordered pair [A025480(n), A348717(n)], or equally, of the ordered pair [A003602(1+n), A246277(n)].
%C A364950 For all i, j:
%C A364950   a(i) = a(j) => A364949(i) = A364949(j),
%C A364950   a(i) = a(j) => A364951(i) = A364951(j).
%H A364950 Antti Karttunen, <a href="/A364950/b364950.txt">Table of n, a(n) for n = 1..65537</a>
%o A364950 (PARI)
%o A364950 up_to = 65537;
%o A364950 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 A364950 A025480(n) = (n>>valuation(n*2+2, 2));
%o A364950 A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
%o A364950 Aux364950(n) = [A025480(n), A348717(n)];
%o A364950 v364950 = rgs_transform(vector(up_to, n, Aux364950(n)));
%o A364950 A364950(n) = v364950[n];
%Y A364950 Cf. A003602, A025480, A246277, A348717, A364949, A364951.
%K A364950 nonn
%O A364950 1,2
%A A364950 _Antti Karttunen_, Aug 17 2023