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.

%I A047699 #18 Nov 09 2018 14:05:27
%S A047699 0,1,4,10,17,29,44,66,89,113,139,170,202,237,273,311,352,394,445,497,
%T A047699 550,605,664,728,796,871,948,1026,1106,1188,1274,1361,1452,1544,1638,
%U A047699 1735,1835,1936,2038,2145,2256,2372,2491,2611,2736,2863,2991
%N 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.
%C A047699 A sparse maximal expulsion set under addition.
%C A047699 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.
%H A047699 Andrew Weimholt, <a href="/A047699/b047699.txt">Table of n, a(n) for n = 0..999</a>
%H A047699 K. S. Brown, <a href="http://www.mathpages.com/home/kmath509/kmath509.htm">Expulsion Sets</a>
%e A047699 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.
%t A047699 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 *)
%Y A047699 Cf. A047705, A047706, A167209.
%K A047699 nonn,easy,nice
%O A047699 0,3
%A A047699 K. S. Brown (ksbrown(AT)seanet.com)
%E A047699 Corrected by _Andrew Weimholt_, Jul 13 2010