A319103 a(n) is the least k > 0 such that A318928(k) = n.

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

Links

Table of n, a(n) for n=0..12.

Rémy Sigrist, PARI program for A319103

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

Adjacent sequences: A319100 A319101 A319102 * A319104 A319105 A319106

Keyword

nonn,base,more

Author

Rémy Sigrist, Sep 10 2018

Extensions

a(11)-a(12) from Hiroaki Yamanouchi, Sep 22 2018

Status

approved