cp's OEIS Frontend

A334867 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A334204(i) = A334204(j) for all i, j >= 1.

%I A334867 #14 Sep 07 2023 16:07:04
%S A334867 1,1,2,1,3,2,4,1,5,3,6,2,6,4,6,1,7,5,8,3,8,6,9,2,5,6,8,4,8,6,10,1,11,
%T A334867 7,9,5,9,8,12,3,13,8,14,6,11,9,15,2,15,5,13,6,9,8,9,4,15,8,16,6,8,10,
%U A334867 17,1,12,11,14,7,14,9,18,5,11,9,19,8,20,12,21,3,14,13,12,8,22,14,21,6,12,11,14,9,14,15,15,2,23,15,14,5,11,13,12,6,14
%N A334867 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A334204(i) = A334204(j) for all i, j >= 1.
%C A334867 Restricted growth sequence transform of the ordered pair [A329697(n), A334204(n)].
%C A334867 For all i, j:
%C A334867   A365388(i) = A365388(j) => a(i) = a(j) => A334873(i) = A334873(j).
%H A334867 Antti Karttunen, <a href="/A334867/b334867.txt">Table of n, a(n) for n = 1..65537</a>
%o A334867 (PARI)
%o A334867 up_to = 65537;
%o A334867 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 A334867 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A334867 A054429(n) = ((3<<#binary(n\2))-n-1);
%o A334867 A163511(n) = if(!n,1,A005940(1+A054429(n)));
%o A334867 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A334867 A334204(n) = A329697(A163511(n));
%o A334867 A334867aux(n) = [A329697(n),A334204(n)];
%o A334867 v334867 = rgs_transform(vector(up_to,n,A334867aux(n)));
%o A334867 A334867(n) = v334867[n];
%Y A334867 Cf. A000079 (positions of ones), A163511, A329697, A334204, A334873.
%Y A334867 Cf. also A318310, A365386, A365388.
%K A334867 nonn,look
%O A334867 1,3
%A A334867 _Antti Karttunen_, Jun 09 2020