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A378604 Lexicographically earliest infinite sequence such that a(i) = a(j) => A033630(i) = A033630(j) and A083206(i) = A083206(j), for all i, j >= 1.

%I A378604 #6 Dec 01 2024 19:54:51
%S A378604 1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,4,1,2,1,1,1,5,1,1,1,2,1,6,1,1,1,1,
%T A378604 1,7,1,1,1,8,1,9,1,1,1,1,1,10,1,1,1,1,1,8,1,3,1,1,1,11,1,1,1,1,1,9,1,
%U A378604 1,1,12,1,13,1,1,1,1,1,14,1,15,1,1,1,16,1,1,1,2,1,17,1,1,1,1,1,18,1,1,1,4,1,14,1,2,1
%N A378604 Lexicographically earliest infinite sequence such that a(i) = a(j) => A033630(i) = A033630(j) and A083206(i) = A083206(j), for all i, j >= 1.
%C A378604 Restricted growth sequence transform of the ordered pair [A033630(n), A083206(n)].
%H A378604 Antti Karttunen, <a href="/A378604/b378604.txt">Table of n, a(n) for n = 1..100000</a>
%o A378604 (PARI)
%o A378604 up_to = 100000;
%o A378604 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 A378604 v033630 = readvec("b033630_to.txt"); \\ Precomputed with A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
%o A378604 A033630(n) = v033630[n];
%o A378604 v083206 = readvec("b083206_to.txt"); \\ Precomputed with A083206(n) = { my(p=1); fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2); };
%o A378604 A083206(n) = v083206[n];
%o A378604 Aux378604(n) = [A033630(n), A083206(n)];
%o A378604 v378604 = rgs_transform(vector(up_to, n, Aux378604(n)));
%o A378604 A378604(n) = v378604[n];
%Y A378604 Cf. A033630, A083206.
%Y A378604 Cf. also A378601, A378602, A378603.
%K A378604 nonn
%O A378604 1,6
%A A378604 _Antti Karttunen_, Dec 01 2024