A022941 a(n) = a(n-1) + c(n-2) for n >= 3, a( ) increasing, given a(1)=1, a(2)=2; where c( ) is complement of a( ).

1, 2, 5, 9, 15, 22, 30, 40, 51, 63, 76, 90, 106, 123, 141, 160, 180, 201, 224, 248, 273, 299, 326, 354, 383, 414, 446, 479, 513, 548, 584, 621, 659, 698, 739, 781, 824, 868, 913, 959, 1006, 1054, 1103, 1153, 1205, 1258, 1312, 1367, 1423, 1480, 1538

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Except for a(2), identical to A022940. - Ivan Neretin, Apr 05 2016

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A143344 (first differences), A156031.

Cf. A005228 and references therein.

Programs

Haskell

import Data.List (delete)
a022941 n = a022941_list !! (n-1)
a022941_list = 1 : 2 : f 2 [3..] where
   f x (z:zs) = y : f y (delete y zs) where y = x + z
-- Reinhard Zumkeller, May 17 2013

Maple

a[1]:=1: a[2]:=2: c[1]:=3: for n from 2 to 70 do c[n]:=c[n-1]+1: for k from 1 to n do if(c[n]<=a[k])then if(c[n]=a[k])then c[n]:=c[n]+1: fi: break: fi: od: a[n+1]:=a[n]+c[n-1]: od: seq(a[n],n=1..70); # Nathaniel Johnston, May 01 2011

Mathematica

Fold[Append[#1, #1[[-1]] + Complement[Range[Max@#1 + 1], #1][[#2]]] &, {1, 2}, Range[50]] (* Ivan Neretin, Apr 04 2016 *)

Extensions

a(27) inserted by Nathaniel Johnston, May 01 2011