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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Feb 11 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A006530(n), A007733(n)].

For all i, j >= 1: A324400(i) = A324400(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A006530, A007733.

Cf. also A324400, A351452, A351454, A351460.

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; };
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ This function from A007733
Aux351453(n) = [A006530(n), A007733(n)];
v351453 = rgs_transform(vector(up_to, n, Aux351453(n)));
A351453(n) = v351453[n];