A331742 Lexicographically earliest infinite sequence such that a(i) = a(j) => A323901(i) = A323901(j) for all i, j.

1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 3, 4, 4, 1, 7, 5, 8, 3, 9, 6, 10, 2, 11, 3, 10, 4, 5, 4, 12, 1, 13, 7, 14, 5, 15, 8, 16, 3, 17, 9, 18, 6, 19, 10, 20, 2, 17, 11, 18, 3, 9, 10, 21, 4, 22, 5, 8, 4, 22, 12, 12, 1, 23, 13, 24, 7, 25, 14, 26, 5, 27, 15, 28, 8, 19, 16, 29, 3, 30, 17, 31, 9, 32, 18, 33, 6, 34, 19, 33, 10, 35, 20, 36, 2, 35, 17, 37, 11, 38, 18, 14, 3, 34

Offset: 0

Author

Antti Karttunen, Feb 05 2020

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of function A323901(n) = A002487(A163511(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 Stern's sequences

Crossrefs

Cf. A002487, A163511, A323901.

Cf. also A286378, A305899, A331743, A331744, A331745.

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; };
v331742 = rgs_transform(vector(1+up_to, n, A323901(n-1)));
A331742(n) = v331742[1+n];

Formula

a(2^n) = 1 for all n >= 0.