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A322316 Lexicographically earliest such sequence a that a(i) = a(j) => A122841(i) = A122841(j) and A244417(i) = A244417(j), for all i, j.

%I A322316 #11 Jun 01 2025 17:34:59
%S A322316 1,2,2,3,1,4,1,5,3,2,1,6,1,2,2,7,1,6,1,3,2,2,1,8,1,2,5,3,1,4,1,9,2,2,
%T A322316 1,10,1,2,2,5,1,4,1,3,3,2,1,11,1,2,2,3,1,8,1,5,2,2,1,6,1,2,3,12,1,4,1,
%U A322316 3,2,2,1,13,1,2,2,3,1,4,1,7,7,2,1,6,1,2,2,5,1,6,1,3,2,2,1,14,1,2,3,3,1,4,1,5,2
%N A322316 Lexicographically earliest such sequence a that a(i) = a(j) => A122841(i) = A122841(j) and A244417(i) = A244417(j), for all i, j.
%C A322316 Restricted growth sequence transform of the ordered pair [A122841(n), A244417(n)].
%C A322316 Essentially also the restricted growth sequence transform of the unordered pair {A007814(n), A007949(n)}.
%C A322316 For all i, j: a(i) = a(j) => A072078(i) = A072078(j).
%H A322316 Antti Karttunen, <a href="/A322316/b322316.txt">Table of n, a(n) for n = 1..19683</a>
%H A322316 Antti Karttunen, <a href="/A322316/a322316.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o A322316 (PARI)
%o A322316 up_to = 65537;
%o A322316 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 A322316 A007814(n) = valuation(n,2);
%o A322316 A007949(n) = valuation(n,3);
%o A322316 A122841(n) = min(A007814(n), A007949(n));
%o A322316 A244417(n) = max(valuation(n,2), valuation(n,3));
%o A322316 v322316 = rgs_transform(vector(up_to, n, [A122841(n), A244417(n)]));
%o A322316 \\ The following is equivalent:
%o A322316 \\ v322316 = rgs_transform(vector(up_to, n, Set([A007814(n), A007949(n)])));
%o A322316 A322316(n) = v322316[n];
%Y A322316 Cf. A007814, A007949, A122841, A244417, A322026, A322317 (ordinal transform).
%K A322316 nonn
%O A322316 1,2
%A A322316 _Antti Karttunen_, Dec 04 2018