login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309797 Lexicographically earliest sequence of positive integers such that for any n > 0 there are no more than a(n) numbers k > 0 such that a(n + k) = a(n + 2*k). 4
1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 3, 3, 2, 2, 2, 4, 2, 4, 5, 4, 1, 1, 1, 1, 3, 3, 3, 1, 6, 6, 6, 7, 5, 3, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 7, 5, 7, 5, 8, 5, 8, 8, 8, 8, 3, 1, 1, 1, 1, 9, 9, 6, 1, 1, 1, 1, 10, 3, 3, 3, 6, 6, 6, 6, 6, 7, 6, 3, 9, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The sequence is well defined as we can always extend the sequence with a number that has not yet appeared.

The number 1 appears infinitely many times in the sequence:

- by contradiction: suppose that m is the index of the last occurrence of 1 in the sequence,

- there is no n > 0 such that n + k = m and n + 2*k = 2*m (with k > 0),

- so we can choose a(2*m) = 1, QED.

This sequence has connections with A003602:

- here we have up to a(n) numbers k such that a(n+k) = a(n+2*k), there we have no such numbers,

- for any v >= 0, let f_v be the lexicographically earliest sequence of positive integers such that there are no more than v numbers k such that f_v(n + k) = f_v(n + 2*k),

- then f_v corresponds to A003602 where all but the first term have been repeated 2*v+1 times.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A309797

Rémy Sigrist, Scatterplot of the first 500000 terms

FORMULA

a(n) >= #{ k>0 such that a(n+k) = a(n+2*k) }.

EXAMPLE

The first terms, alongside the corresponding k's, are:

  n   a(n)  k's

  --  ----  ----------

   1     1  {1}

   2     1  {1}

   3     1  {2}

   4     1  {1}

   5     2  {1, 3}

   6     2  {2, 14}

   7     2  {1, 2}

   8     1  {1}

   9     1  {1}

  10     1  {4}

  11     1  {1}

  12     3  {2, 3, 68}

  13     3  {1, 4, 22}

  14     2  {1, 2}

PROG

(PARI) See Links section.

CROSSREFS

Cf. A003602, A329268 (positions of 1).

Sequence in context: A029432 A073426 A232439 * A199840 A126067 A327490

Adjacent sequences:  A309794 A309795 A309796 * A309798 A309799 A309800

KEYWORD

nonn,look

AUTHOR

Rémy Sigrist, Nov 11 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 9 10:32 EDT 2020. Contains 333348 sequences. (Running on oeis4.)