A318310 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000120(i) = A000120(j) and A033879(i) = A033879(j), for all i, j >= 0.

1, 1, 2, 1, 3, 4, 5, 1, 6, 2, 7, 8, 9, 10, 11, 1, 12, 13, 14, 15, 7, 16, 17, 18, 19, 7, 20, 21, 22, 23, 24, 1, 25, 26, 27, 28, 29, 30, 17, 31, 32, 33, 34, 10, 35, 36, 37, 38, 39, 40, 41, 5, 42, 23, 43, 44, 45, 46, 47, 48, 49, 50, 51, 1, 52, 18, 53, 54, 55, 56, 57, 58, 59, 60, 46, 9, 61, 23, 62, 63, 39, 64, 65, 66, 67, 68, 69, 56, 70, 71, 72, 73, 47, 74

Offset

1,3

Comments

Restricted growth sequence transform of ordered pair [A000120(n), A033879(n)], or equally, of ordered pair [A000120(n), A294898(n)].

For all i, j:

A318311(i) = A318311(j) => a(i) = a(j),

a(i) = a(j) => A286449(i) = A286449(j),

a(i) = a(j) => A294898(i) = A294898(j).

In the scatter plot one can see the effects of both base-2 related A000120 (binary weight of n) and prime factorization related A033879 (deficiency of n) graphically mixed: from the former, a square grid pattern, and from the latter the black rays that emanate from the origin. The same is true for A323898, while in the ordinal transform of this sequence, A331184, such effects are harder to visually discern. - Antti Karttunen, Jan 13 2020

Links

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

Prog

(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; };
A318310aux(n) = [hammingweight(n), (2*n) - sigma(n)];
v318310 = rgs_transform(vector(up_to, n, A318310aux(n)));
A318310(n) = v318310[n];

Crossrefs

Cf. A000120, A033879, A286449, A295881, A295882, A294898.

Cf. A318311, A323889, A323892, A323898, A324344, A324380, A324390 for similar constructions.

Cf. A331184 (ordinal transform).

Sequence in context: A088267 A364577 A286449 * A336925 A331744 A323892

Adjacent sequences: A318307 A318308 A318309 * A318311 A318312 A318313

Keyword

nonn,look

Author

Antti Karttunen, Aug 25 2018

Extensions

Name changed by Antti Karttunen, Jan 13 2020

Status

approved