A143344 -id:A143344 - cp's OEIS frontend

A156031 Alternate A022941 and A143344.

1, 2, 3, 5, 4, 9, 6, 15, 7, 22, 8, 30, 10, 40, 11, 51, 12, 63, 13, 76, 14, 90, 16, 106, 17, 123, 18, 141, 19, 160, 20, 180, 21, 201, 23, 224, 24, 248, 25, 273, 26, 299, 27, 326, 28, 354, 29, 383, 31, 414, 32, 446, 33, 479, 34, 513, 35, 548, 36, 584, 37, 621, 38, 659, 39, 698

Offset: 1

N. J. A. Sloane, Nov 01 2009, based on a posting by Eric Angelini to the Sequence Fans Mailing List

nonn

Eric Angelini's definition was: start with 1,2,3; then alternately adjoin either the sum of the last two terms or the smallest number not yet in the sequence.

M. F. Hasler, Table of n, a(n) for n = 1..2001

Cf. A022941, A143344, A167151, A005228, A030124.

import Data.List (transpose)
a156031 n = a156031_list !! n
a156031_list = tail $ concat (transpose [a022941_list, a143344_list])
-- Reinhard Zumkeller, May 17 2013

f="b156031.txt"; used=[]; write(f,c=1," ",b=1);a=1; for(i=1,1e3, used=setunion(used,Set(a+=b)); while(setsearch(used,b++), used=setminus(used,Set(b))); write(f,c++," "a"\n",c++," "b)) \\ M. F. Hasler, Nov 01 2009

A167151 a(2n+1) = a(2n) + a(2n-1), a(2n)=least number not yet in the sequence, a(1)=1.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 12, 6, 18, 8, 26, 9, 35, 10, 45, 11, 56, 13, 69, 14, 83, 15, 98, 16, 114, 17, 131, 19, 150, 20, 170, 21, 191, 22, 213, 23, 236, 24, 260, 25, 285, 27, 312, 28, 340, 29, 369, 30, 399, 31, 430, 32, 462, 33, 495, 34, 529, 36, 565, 37, 602, 38, 640, 39, 679

Offset: 0

M. F. Hasler, Nov 01 2009

Lexicographically earliest reordering of the nonnegative integers (can be extended by symmetry to a permutation of all integers) such that a(2n+1) = a(2n) + a(2n-1).

Cf. A022941, A143344, A156031.

Cf. A225850 (inverse).

import Data.List (transpose)
a167151 n = a167151_list !! n
a167151_list = 0 : concat (transpose [a005228_list, a030124_list])
-- Reinhard Zumkeller, May 17 2013

a[0] = 0; a[1] = 1;
a[n_?OddQ] := a[n] = a[n - 1] + a[n - 2];
a[n_?EvenQ] := a[n] = For[k = 2, True, k++,
     If[FreeQ[Array[a, n - 1], k], Return[k]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 02 2021 *)

{used=[]; print1(b=0); a=1; for(i=1,99, used=setunion(used,Set(a+=b)); while(setsearch(used,b++), used=setminus(used,Set(b))); print1(", "a", "b))}

a(2n-1) = A005228(n); a(2n) = A030124(n).

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( ).

Original entry on oeis.org

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

Clark Kimberling

nonn

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

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

Cf. A143344 (first differences), A156031.

Cf. A005228 and references therein.

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

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

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

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

cp's OEIS Frontend

A156031 Alternate A022941 and A143344.

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A167151 a(2n+1) = a(2n) + a(2n-1), a(2n)=least number not yet in the sequence, a(1)=1.

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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( ).

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