A324380 Lexicographically earliest positive sequence such that a(i) = a(j) => A069010(i) = A069010(j) and A324386(i) = A324386(j), for all i, j >= 0.

1, 2, 3, 2, 3, 4, 3, 2, 5, 6, 6, 4, 3, 7, 8, 2, 3, 6, 9, 6, 6, 10, 11, 4, 12, 7, 13, 7, 14, 13, 12, 2, 5, 6, 7, 4, 9, 10, 9, 6, 7, 15, 16, 17, 18, 19, 18, 4, 12, 18, 6, 7, 20, 21, 22, 7, 23, 24, 25, 7, 26, 24, 26, 2, 8, 9, 9, 6, 11, 15, 7, 9, 11, 16, 27, 28, 25, 29, 25, 6, 18, 30, 21, 15, 31, 32, 19, 15, 33, 34, 16, 15, 35, 29, 33, 4, 36, 20, 24, 20, 37, 30, 24, 11

Offset: 0

Author

Antti Karttunen, Feb 27 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A069010(n), A324386(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A069010, A324386.

Cf. also A324343, A324344, A324390.

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; };
A069010(n) = ((1 + (hammingweight(bitxor(n, n>>1)))) >> 1); \\ From A069010
Aux324380(n) = [A069010(n), A324386(n)]; \\ Code for A324386 available in that entry.
v324380 = rgs_transform(vector(1+up_to,n,Aux324380(n-1)));
A324380(n) = v324380[1+n];

Formula

a(A000225(n)) = 2 for all n >= 1.