A332901 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A332896(i)) = A278222(A332896(j)) for all i, j.

1, 1, 2, 1, 2, 2, 3, 1, 1, 2, 4, 2, 3, 3, 3, 1, 4, 1, 5, 2, 2, 4, 6, 2, 1, 3, 2, 3, 5, 3, 7, 1, 3, 4, 8, 1, 6, 5, 4, 2, 7, 2, 9, 4, 2, 6, 10, 2, 1, 1, 5, 3, 9, 2, 11, 3, 4, 5, 12, 3, 10, 7, 3, 1, 2, 3, 13, 4, 5, 8, 14, 1, 12, 6, 2, 5, 2, 4, 15, 2, 1, 7, 16, 2, 3, 9, 6, 4, 13, 2, 17, 6, 6, 10, 18, 2, 14, 1, 4, 1, 15, 5, 19, 3, 3

Offset: 1

Author

Antti Karttunen, Mar 04 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of A278222(A332896(n)).

This is a variant of A292583: Instead of runs of numbers of the form 4k+3 encountered on trajectories of the standard Doudna-tree (A005940), this relates to the corresponding trajectories in A332815-tree. See comments in A292583.

For all i, j:

a(i) = a(j) => A053866(i) = A053866(j),

a(i) = a(j) => A332898(i) = A332898(j).

Links

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

Crossrefs

Cf. A053866, A278222, A332896, A332898, A332900.

Cf. A028982 (positions of ones).

Cf. also A292583.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
v332901 = rgs_transform(vector(up_to,n,A278222(A332896(n))));
A332901(n) = v332901[n];