A322316 Lexicographically earliest such sequence a that a(i) = a(j) => A122841(i) = A122841(j) and A244417(i) = A244417(j), for all i, j.

1, 2, 2, 3, 1, 4, 1, 5, 3, 2, 1, 6, 1, 2, 2, 7, 1, 6, 1, 3, 2, 2, 1, 8, 1, 2, 5, 3, 1, 4, 1, 9, 2, 2, 1, 10, 1, 2, 2, 5, 1, 4, 1, 3, 3, 2, 1, 11, 1, 2, 2, 3, 1, 8, 1, 5, 2, 2, 1, 6, 1, 2, 3, 12, 1, 4, 1, 3, 2, 2, 1, 13, 1, 2, 2, 3, 1, 4, 1, 7, 7, 2, 1, 6, 1, 2, 2, 5, 1, 6, 1, 3, 2, 2, 1, 14, 1, 2, 3, 3, 1, 4, 1, 5, 2

Offset: 1

Author

Antti Karttunen, Dec 04 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A122841(n), A244417(n)].

Essentially also the restricted growth sequence transform of the unordered pair {A007814(n), A007949(n)}.

For all i, j: a(i) = a(j) => A072078(i) = A072078(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..19683
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A007814, A007949, A122841, A244417, A322026, A322317 (ordinal transform).

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; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A122841(n) = min(A007814(n), A007949(n));
A244417(n) = max(valuation(n,2), valuation(n,3));
v322316 = rgs_transform(vector(up_to, n, [A122841(n), A244417(n)]));
\\ The following is equivalent:
\\ v322316 = rgs_transform(vector(up_to, n, Set([A007814(n), A007949(n)])));
A322316(n) = v322316[n];