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A319103
a(n) is the least k > 0 such that A318928(k) = n.
4
1, 3, 2, 4, 11, 18, 75, 621, 9638, 1264052, 1294752365, 20699153586797, 43409394810283725529
OFFSET
0,2
COMMENTS
This sequence is well defined and infinite:
- for any n > 1, we can build a number m such that A318928(m) = 1 + A318928(n),
- let (b_1, ..., b_k) be the binary representation of n,
- let r_1 = 1, and for i = 1..k-1: r_{i+1} = r_i if b_{i+1} = b_i and r_{i+1} = 2 - r_i otherwise,
- the number m whose run lengths in binary representation are (r_1, ..., r_k) satisfies A318928(m) = 1 + A318928(n).
a(11) <= 42414573279593.
Here A318928(1) is considered to be 0, which differs from the current definition of A318928. However, I think it is quite natural to define A318928(1) to be 0. - Hiroaki Yamanouchi, Sep 22 2018
EXAMPLE
The first terms of A318928, alongside the corresponding terms in this sequence, are:
n A318928(n) Corresponding terms
-- ---------- -------------------
1 0 a(0) = 1
2 2 a(2) = 2
3 1 a(1) = 3
4 3 a(3) = 4
5 2
6 3
7 1
8 3
9 3
10 2
11 4 a(4) = 11
12 2
13 4
PROG
(PARI) See Links section.
CROSSREFS
Cf. A318928.
See A319417, A319418 for record values in A318928.
Sequence in context: A277743 A296099 A349853 * A332647 A290333 A137824
KEYWORD
nonn,base,more
AUTHOR
Rémy Sigrist, Sep 10 2018
EXTENSIONS
a(11)-a(12) from Hiroaki Yamanouchi, Sep 22 2018
STATUS
approved