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

0,2

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

Formula

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

Prog

(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];

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.

Sequence in context: A286378 A331745 A103391 * A366802 A178804 A322355

Adjacent sequences: A331740 A331741 A331742 * A331744 A331745 A331746

Keyword

nonn

Author

Antti Karttunen, Feb 05 2020

Status

approved