A047699 - OEIS

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

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OFFSET

0,3

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.

LINKS

Andrew Weimholt, Table of n, a(n) for n = 0..999

K. S. Brown, Expulsion Sets

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A047705, A047706, A167209.

Sequence in context: A008022 A213497 A339576 * A167209 A096077 A008147

Adjacent sequences: A047696 A047697 A047698 * A047700 A047701 A047702

KEYWORD

nonn,easy,nice

AUTHOR

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

EXTENSIONS

Corrected by Andrew Weimholt, Jul 13 2010

STATUS

approved