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

Author

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

Keywords

• nonn
• easy
• nice

Comments

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A047705, A047706, A167209.

Programs

Mathematica

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 *)

Extensions

Corrected by Andrew Weimholt, Jul 13 2010