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A364951 Lexicographically earliest infinite sequence such that a(i) = a(j) => A025480(i) = A025480(j) and A046523(i) = A046523(j) for all i, j >= 1.

%I A364951 #10 Aug 17 2023 19:26:11
%S A364951 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 A364951 23,24,3,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,2,40,41,42,43,
%U A364951 44,45,46,5,47,48,49,23,50,51,52,53,54,55,56,57,58,27,59,13,60,61,62,14,63,31,64,15,65,66,67,34,68
%N A364951 Lexicographically earliest infinite sequence such that a(i) = a(j) => A025480(i) = A025480(j) and A046523(i) = A046523(j) for all i, j >= 1.
%C A364951 Restricted growth sequence transform of the ordered pair [A025480(n), A046523(n)], or equally, of the ordered pair [A003602(1+n), A101296(n)].
%C A364951 For all i, j: A364950(i) = A364950(j) => a(i) = a(j).
%H A364951 Antti Karttunen, <a href="/A364951/b364951.txt">Table of n, a(n) for n = 1..65537</a>
%o A364951 (PARI)
%o A364951 up_to = 65537;
%o A364951 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 A364951 A025480(n) = (n>>valuation(n*2+2, 2));
%o A364951 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A364951 Aux364951(n) = [A025480(n), A046523(n)];
%o A364951 v364951 = rgs_transform(vector(up_to, n, Aux364951(n)));
%o A364951 A364951(n) = v364951[n];
%Y A364951 Cf. A003602, A025480, A046523, A101296, A364950.
%K A364951 nonn
%O A364951 1,2
%A A364951 _Antti Karttunen_, Aug 17 2023