A331743 Lexicographically earliest infinite sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A323901(i) = A323901(j) for all i, j.

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

Offset: 0

Author

Antti Karttunen, Feb 05 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A002487(n), A002487(A163511(n))].

For all i, j:

a(i) = a(j) => A331748(i) = A331748(j),

a(i) = a(j) => A331749(i) = A331749(j).

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 Stern's sequences

Crossrefs

Cf. A002487, A163511, A323901, A324400, A331742, A331744, A331748, A331749.

Differs from A331745 for the first time at n=77, where a(77) = 40, while A331745(77) = 24.

Differs from A103391(1+n) for the first time at n=191, where a(191) = 23, while A103391(192) = 97.

Programs

PARI

\\ Needs also code from A323901.
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; };
Aux331743(n) = [A002487(n), A323901(n)];
v331743 = rgs_transform(vector(1+up_to, n, Aux331743(n-1)));
A331743(n) = v331743[1+n];

Formula

a(2^n) = 2 for all n >= 0.