A366886 - OEIS

%I #11 Jan 03 2024 16:34:15

%S 1,1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,

%T 3,1,16,9,17,5,18,10,19,3,20,11,21,6,22,12,23,2,24,13,25,7,26,14,27,4,

%U 27,15,13,8,14,3,28,1,29,16,30,9,31,17,32,5,33,18,34,10,35,19,36,3,37,20,38,11,39,21,40,6

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A366885(i) = A366885(j) for all i, j >= 0.

%C Restricted growth sequence transform of A366885.

%C Albeit quite ugly, the scatter plot is still interesting. - _Antti Karttunen_, Jan 03 2024

%H Antti Karttunen, <a href="/A366886/b366886.txt">Table of n, a(n) for n = 0..65537</a>

%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 A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));

%o A366885(n) = A347385(A163511(n));

%o v366886 = rgs_transform(vector(1+up_to,n,A366885(n-1)));

%o A366886(n) = v366886[1+n];

%Y Cf. A163511, A347385, A366885.

%Y Cf. also A366806, A366881, A366891 (compare the scatter plots).

%K nonn,look

%O 0,4

%A _Antti Karttunen_, Nov 04 2023