A047699 -id:A047699 - cp's OEIS frontend

A047705 First differences of A047699.

1, 3, 6, 7, 12, 15, 22, 23, 24, 26, 31, 32, 35, 36, 38, 41, 42, 51, 52, 53, 55, 59, 64, 68, 75, 77, 78, 80, 82, 86, 87, 91, 92, 94, 97, 100, 101, 102, 107, 111, 116, 119, 120, 125, 127, 128, 131, 137, 144, 146, 147, 151, 154, 159, 161, 163, 164, 165

Offset: 0

N. J. A. Sloane

nonn

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

Cf. A047699, A047706.

Corrected by Zak Seidov and 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

N. J. A. Sloane

nonn

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

Cf. A047699, A047705.

Corrected by Zak Seidov and Andrew Weimholt, Jul 13 2010

A167209 a(0) = 0; for n>=0, a(n+1) = a(n) + x where x is the smallest nonnegative number which is not equal to a(i) +/- a(k) or a(i)/2 for any 0<=i<=n, 0<=k<=n.

Original entry on oeis.org

0, 1, 4, 10, 17, 29, 44, 67, 91, 117, 148, 180, 215, 251, 288, 329, 371, 420, 471, 523, 576, 631, 687, 746, 806, 870, 935, 1004, 1074, 1146, 1221, 1297, 1376, 1456, 1538, 1623, 1709, 1802, 1896, 1993, 2092, 2194, 2300, 2409, 2519, 2631, 2753, 2876, 3001, 3127, 3255, 3385, 3518, 3655, 3796, 3939

Offset: 0

N. J. A. Sloane, Sep 03 2014

nonn

A maximal expulsion set of natural numbers.

Note that this definition is different from that of A047699.

Rémy Sigrist, Table of n, a(n) for n = 0..10000
K. S. Brown, Expulsion Sets
Rémy Sigrist, C program for A167209

Cf. A169799, A169820, A047699.

C
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See Links section.
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Initial value changed to a(0)=0 by N. J. A. Sloane, Feb 18 2019 (otherwise the definition did not match the terms).

A175569 a(0)=2; for n>=0, a(n+1) = a(n) + x where x is the smallest positive number which is not equal to a(i) +/- a(k) for any i, k, 0<=k<=i<=n.

Original entry on oeis.org

2, 3, 10, 19, 30, 44, 59, 77, 100, 124, 150, 181, 216, 252, 289, 328, 371, 416, 464, 515, 567, 620, 675, 739, 807, 879, 962, 1046, 1131, 1217, 1312, 1413, 1522, 1633, 1746, 1861, 1978, 2101, 2226, 2355, 2488, 2623, 2761, 2902, 3044, 3189, 3335, 3484, 3642

Offset: 0

Zak Seidov, Jul 14 2010

nonn

The same as A047699 except for a(0)=2.

Cf. A047699.

a=2;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

Offset corrected. - R. J. Mathar, Jun 19 2021

cp's OEIS Frontend

A047705 First differences of A047699.

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A047706 Second differences of A047699.

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A167209 a(0) = 0; for n>=0, a(n+1) = a(n) + x where x is the smallest nonnegative number which is not equal to a(i) +/- a(k) or a(i)/2 for any 0<=i<=n, 0<=k<=n.

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C

Extensions

A175569 a(0)=2; for n>=0, a(n+1) = a(n) + x where x is the smallest positive number which is not equal to a(i) +/- a(k) for any i, k, 0<=k<=i<=n.

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Mathematica

Extensions