cp's OEIS Frontend

A351453 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A007733(i) = A007733(j) for all i, j >= 1.

%I A351453 #8 Feb 11 2022 17:49:14
%S A351453 1,2,3,2,4,3,5,2,6,4,7,3,8,5,4,2,9,6,10,4,11,7,12,3,13,8,14,5,15,4,16,
%T A351453 2,7,9,17,6,18,10,8,4,19,11,20,7,21,12,22,3,23,13,9,8,24,14,25,5,10,
%U A351453 15,26,4,27,16,11,2,8,7,28,9,29,17,30,6,31,18,13,10,32,8,33,4,34,19,35,11,9,20,15,7,36,21,8,12,37,22,38,3,39,23,32,13,40,9,41,8,17
%N A351453 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A007733(i) = A007733(j) for all i, j >= 1.
%C A351453 Restricted growth sequence transform of the ordered pair [A006530(n), A007733(n)].
%C A351453 For all i, j >= 1: A324400(i) = A324400(j) => a(i) = a(j).
%H A351453 Antti Karttunen, <a href="/A351453/b351453.txt">Table of n, a(n) for n = 1..65537</a>
%o A351453 (PARI)
%o A351453 up_to = 65537;
%o A351453 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 A351453 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A351453 A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ This function from A007733
%o A351453 Aux351453(n) = [A006530(n), A007733(n)];
%o A351453 v351453 = rgs_transform(vector(up_to, n, Aux351453(n)));
%o A351453 A351453(n) = v351453[n];
%Y A351453 Cf. A006530, A007733.
%Y A351453 Cf. also A324400, A351452, A351454, A351460.
%K A351453 nonn
%O A351453 1,2
%A A351453 _Antti Karttunen_, Feb 11 2022