A167209 -id:A167209 - cp's OEIS frontend

A169799 First differences of A167209.

1, 3, 6, 7, 12, 15, 23, 24, 26, 31, 32, 35, 36, 37, 41, 42, 49, 51, 52, 53, 55, 56, 59, 60, 64, 65, 69, 70, 72, 75, 76, 79, 80, 82, 85, 86, 93, 94, 97, 99, 102, 106, 109, 110, 112, 122, 123, 125, 126, 128, 130, 133, 137, 141, 143, 145, 150, 153, 154, 157, 166, 168, 172, 173, 174, 178, 185, 188, 193, 195, 199, 200

Offset: 1

N. J. A. Sloane, Sep 03 2014

nonn

K. S. Brown, Expulsion Sets

Cf. A167209, A169820.

Definition changed because of new offset in A167209. - N. J. A. Sloane, Feb 18 2019

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.

Original entry on oeis.org

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

A169820 1 followed by first differences of A169799.

Original entry on oeis.org

1, 2, 3, 1, 5, 3, 8, 1, 2, 5, 1, 3, 1, 1, 4, 1, 7, 2, 1, 1, 2, 1, 3, 1, 4, 1, 4, 1, 2, 3, 1, 3, 1, 2, 3, 1, 7, 1, 3, 2, 3, 4, 3, 1, 2, 10, 1, 2, 1, 2, 2, 3, 4, 4, 2, 2, 5, 3, 1, 3, 9, 2, 4, 1, 1, 4, 7, 3, 5, 2, 4, 1, 2, 1, 3, 7, 5, 8, 1, 1, 1, 2, 2, 3, 1, 5, 1, 3, 3, 8, 9, 3, 5, 3, 2, 2, 18, 2, 8, 4

Offset: 1

Entry revised by N. J. A. Sloane, Sep 03 2014

nonn

Essentially the second differences of A167209.

K. S. Brown, Expulsion Sets

Cf. A167209, A169799.

cp's OEIS Frontend

A169799 First differences of A167209.

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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.

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Mathematica

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A169820 1 followed by first differences of A169799.

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