A369065 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344026(i) = A344026(j) for all i, j >= 0.

1, 2, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 10, 15, 6, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 2, 27, 19, 13, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 2, 55, 9, 56, 31, 57, 23, 34, 58, 59, 60, 61, 62, 63, 50, 64, 15, 65, 66

Offset: 0

Author

Antti Karttunen, Jan 16 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of A344026, i.e., of the arithmetic derivative (A003415) as reordered by the Doudna sequence (A005940).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A003415, A005940, A344026.

Cf. also A366802, A369067.

Programs

PARI

up_to = 65537;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344026(n) = A003415(A005940(1+n));
v369065 = rgs_transform(vector(1+up_to,n,A344026(n-1)));
A369065(n) = v369065[1+n];