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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 (list; graph; refs; listen; history; text; internal format)
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: A266189 A277743 A296099 * A290333 A137824 A019321

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

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Last modified March 20 09:23 EDT 2019. Contains 321345 sequences. (Running on oeis4.)