Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #17 Sep 10 2023 18:08:58
%S 1,2,2,1,2,3,1,4,2,5,3,6,1,7,4,8,2,9,5,10,3,6,6,11,1,3,7,12,4,13,8,14,
%T 2,9,9,10,5,15,10,16,3,17,6,18,6,11,11,19,1,20,3,21,7,22,12,8,4,13,13,
%U 23,8,24,14,25,2,26,9,27,9,28,10,29,5,30,15,16,10,31,16,32,3,6,17,33,6,31,18,34,6,35,11
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A364492(i) = A364492(j) for all i, j >= 0, where A364492(n) is the denominator of n / A163511(n).
%C Restricted growth sequence transform of A364492.
%C Question: Which sets of numbers cause the finite branches that grow off-angle from the rays emanating from the origin in the scatter plot, and why the sudden bends in some of them? Compare also to the scatter plot of A365431.
%H Antti Karttunen, <a href="/A365393/b365393.txt">Table of n, a(n) for n = 0..65537</a>
%F For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%o (PARI)
%o up_to = 65537;
%o 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 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A364492(n) = { my(u=A163511(n)); (u/gcd(n, u)); };
%o v365393 = rgs_transform(vector(1+up_to,n,A364492(n-1)));
%o A365393(n) = v365393[1+n];
%Y Cf. A000265, A003602, A163511, A364255, A364492.
%Y Cf. also A365384, A365431.
%K nonn,look
%O 0,2
%A _Antti Karttunen_, Sep 06 2023