A094064 Sequences has the properties shown in the Comments lines.

2, 1, 5, 4, 3, 10, 9, 8, 7, 6, 17, 16, 15, 14, 13, 12, 11, 26, 25, 24, 23, 22, 21, 20, 19, 18, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 82

Offset

0,1

Comments

It contains an infinite increasing subsequence.

For each k there is a decreasing subsequence of length > k but no infinite decreasing subsequence.

For each n the first n^2 + 1 terms contain a decreasing subsequence of length n + 1 but no increasing subsequence of length n + 1.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

P. Erdõs, G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463-470; Zentralblatt 12,270.

Lajos Pinter, On monotone subsequences, Math. Gaz., 88 (#511, 2004), 110-111.

Formula

G.f. (3 + 5*x^2 + 4*x*Sum_{n>=2} n*x^(n^2))/(1-x) - 1/(1-x)^2. - Robert Israel, Jan 13 2016

Maple

A[0]:= 2:
A[1]:= 1:
for n from 1 to 9 do
   for i from 1 to 2*n+1 do
     A[n^2+i]:= (n+1)^2+2-i
od od:
seq(A[i], i=0..100); # Robert Israel, Jan 13 2016

Crossrefs

Sequence in context: A280513 A185023 A061579 * A343809 A159930 A058344

Adjacent sequences: A094061 A094062 A094063 * A094065 A094066 A094067

Keyword

nonn

Author

R. K. Guy, May 01 2004

Status

approved