A047705 -id:A047705 - cp's OEIS frontend

A047699 a(0) = 0; for n >= 0, a(n+1) = a(n) + x where x is the smallest nonnegative number that is not equal to a(i) +- a(k) for any 0 <= i <= n, 0 <= k <= n.

0, 1, 4, 10, 17, 29, 44, 66, 89, 113, 139, 170, 202, 237, 273, 311, 352, 394, 445, 497, 550, 605, 664, 728, 796, 871, 948, 1026, 1106, 1188, 1274, 1361, 1452, 1544, 1638, 1735, 1835, 1936, 2038, 2145, 2256, 2372, 2491, 2611, 2736, 2863, 2991

Offset: 0

K. S. Brown (ksbrown(AT)seanet.com)

A sparse maximal expulsion set under addition.

Note that this is not the sparse expulsion set constructed in Kevin Brown's article, which is A167209. That sequence has 67 where this one has 66.

			After {0,1,4,10}, 0, 1, 1 + 1, 4, 4 - 1, 1 + 4, 10 - 4, etc. are excluded, but 7 is not, so next term is 10 + 7 = 17.

Andrew Weimholt, Table of n, a(n) for n = 0..999
K. S. Brown, Expulsion Sets

Cf. A047705, A047706, A167209.

a=0;s={a};X=Complement[Range[10^4],{0,a,2a}]; Do[b=a+X[[1]];X=Complement[X,s+b,b-s,{b,2b}];AppendTo[s,b];a=b,{100}];s (* Zak Seidov, Jul 14 2010 *)

Corrected by Andrew Weimholt, Jul 13 2010

A047706 Second differences of A047699.

Original entry on oeis.org

2, 3, 1, 5, 3, 7, 1, 1, 2, 5, 1, 3, 1, 2, 3, 1, 9, 1, 1, 2, 4, 5, 4, 7, 2, 1, 2, 2, 4, 1, 4, 1, 2, 3, 3, 1, 1, 5, 4, 5, 3, 1, 5, 2, 1, 3, 6, 7, 2, 1, 4, 3, 5, 2, 2, 1, 1, 10, 1, 1, 4, 7, 1, 1, 4, 1, 1, 4, 4, 6, 5, 1, 1, 4, 2, 2, 7, 2, 8, 7, 1, 1, 6, 1, 3, 1, 3, 6, 5, 3, 1, 5, 2, 1, 1, 3, 4, 1, 3, 4

Offset: 0