login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020658 Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 7. 29
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is different from A047304: note the gap between 41 and 50. - M. F. Hasler, Oct 07 2014

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n)=A020657(n)+1. - M. F. Hasler, Oct 07 2014

MAPLE

Noap:= proc(N, m)

# N terms of earliest increasing seq with no m-term arithmetic progression

local A, forbid, n, c, ds, j;

A:= Vector(N):

A[1..m-1]:= <($1..m-1)>:

forbid:= {m}:

for n from m to N do

  c:= min({$A[n-1]+1..max(max(forbid)+1, A[n-1]+1)} minus forbid);

  A[n]:= c;

  ds:= convert(map(t -> c-t, A[m-2..n-1]), set);

  for j from m-2 to 2 by -1 do

    ds:= ds intersect convert(map(t -> (c-t)/j, A[m-j-1..n-j]), set);

    if ds = {} then break fi;

  od;

  forbid:= select(`>`, forbid, c) union map(`+`, ds, c);

od:

convert(A, list)

end proc:

Noap(100, 7); # Robert Israel, Jan 04 2016

CROSSREFS

Cf. A047304.

Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):

3-term AP: A005836 (>=0), A003278 (>0);

4-term AP: A005839 (>=0), A005837 (>0);

5-term AP: A020654 (>=0), A020655 (>0);

6-term AP: A020656 (>=0), A005838 (>0);

7-term AP: A020657 (>=0), A020658 (>0);

8-term AP: A020659 (>=0), A020660 (>0);

9-term AP: A020661 (>=0), A020662 (>0);

10-term AP: A020663 (>=0), A020664 (>0).

Sequence in context: A187396 A020659 A047304 * A195178 A043092 A023801

Adjacent sequences:  A020655 A020656 A020657 * A020659 A020660 A020661

KEYWORD

nonn

AUTHOR

David W. Wilson

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 21:33 EST 2018. Contains 299628 sequences. (Running on oeis4.)