A094870 a(1)=1; for n > 1, a(n) is the minimal positive integer t not equal to a(1), ..., a(n-1) such that t - a(n-i) is not equal to a(n-i) - a(n-2i) for all 1 <= i < n/2.

1, 2, 4, 3, 5, 6, 8, 7, 10, 9, 13, 12, 14, 11, 17, 16, 22, 15, 23, 18, 21, 20, 25, 24, 26, 19, 28, 27, 29, 36, 32, 31, 33, 39, 38, 34, 41, 30, 37, 35, 44, 48, 42, 40, 43, 50, 46, 52, 47, 45, 54, 49, 56, 58, 57, 51, 61, 53, 59, 63, 60, 68, 64, 62, 70, 55, 65, 67, 73, 69, 83, 76

Offset

1,2

Comments

3n/8 <= a(n) < 3n/2 (P. Hegarty).

Conjecture: lim_{n->infinity} a(n)/n = 1 (P. Hegarty).

The Hegarty paper shows that this is a permutation. - Franklin T. Adams-Watters, May 26 2014

Graphically, the sequence {a(n)-n} resembles A293862 (see illustration in Links section). - Rémy Sigrist, Feb 06 2020

Links

Carl R. White, Table of n, a(n) for n = 1..10000

Peter Hegarty, Permutations avoiding arithmetic patterns, The Electronic Journal of Combinatorics, 11 (2004), #R39.

Rémy Sigrist, Scatterplot of (n, a(n)-n) for n = 1..500000

Index entries related to non-averaging sequences

Example

a(3)=4 because it can't be 1=a(1), 2=a(2) and 3=2*a(3-1)-a(3-2).

Maple

A:=proc(n) option remember; local t, S, i; S:={$1..1000} minus {seq(A(i), i=1..n-1)}; t:=min(S[]); i:=1; while i<floor((n+1)/2) do if t-A(n-i)=A(n-i)-A(n-2*i) then S:=S minus {t}; t:=min(S[]); i:=1 else i:=i+1 fi od; t end: A(1):=1: seq(A(n), n=1..200);

Mathematica

a[n_] := a[n] = Module[{t, S, i}, S = Union[Range[1000] ~Complement~ Array[a, n-1]]; t = Min[S]; i = 1; While[i < Floor[(n+1)/2], If[t-a[n-i] == a[n-i] - a[n-2i], S = S ~Complement~ {t}; t = Min[S]; i = 1, i++]]; t]; a[1] = 1;
Table[a[n], {n, 1, 200}] (* Jean-François Alcover, Sep 20 2019, from Maple *)

Crossrefs

Cf. A095689 (inverse permutation), A229037, A293862.

Sequence in context: A259570 A334672 A095690 * A075618 A095689 A083194

Adjacent sequences: A094867 A094868 A094869 * A094871 A094872 A094873

Keyword

easy,nonn

Author

Alec Mihailovs (alec(AT)mihailovs.com), Jun 16 2004

Status

approved