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A369062 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344005(i) = A344005(j) and A345992(i) = A345992(j), for all i, j >= 1.

%I A369062 #6 Jan 21 2024 18:10:52
%S A369062 1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
%T A369062 26,27,28,14,29,30,31,32,33,34,35,36,37,38,39,40,41,31,42,43,44,45,46,
%U A369062 47,48,49,50,51,52,27,53,54,55,56,57,58,59,60,61,31,62,63,64,65,66,23,67,68,69,70,71,72,73,38,74,75,76,77,78,79,80,81,82,42,83,64
%N A369062 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344005(i) = A344005(j) and A345992(i) = A345992(j), for all i, j >= 1.
%C A369062 Restricted growth sequence transform of the ordered pair [A344005(n), A345992(n)], or equally, of the pair [A344005(n), A345998(n)], or equally, of the pair [A345992(n), A345998(n)].
%H A369062 Antti Karttunen, <a href="/A369062/b369062.txt">Table of n, a(n) for n = 1..65537</a>
%o A369062 (PARI)
%o A369062 up_to = 65537;
%o A369062 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 A369062 A344005(n) = { my(m=1); while((m*(m+1)) % n, m++); m; };
%o A369062 Aux369062(n) = { my(u=A344005(n)); [u, gcd(n,u)]; };
%o A369062 v369062 = rgs_transform(vector(up_to, n, Aux369062(n)));
%o A369062 A369062(n) = v369062[n];
%Y A369062 Cf. A344005, A345992, A345998.
%Y A369062 Cf. also A368693.
%K A369062 nonn
%O A369062 1,3
%A A369062 _Antti Karttunen_, Jan 21 2024