This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
For n = 5, the a(5) = 4 sequences are 5 * 6 * 9 * 10 * 15 * 18 = 90^3, 5 * 6 * 8 * 9 * 10 * 15 * 18 = 180^3, 5 * 10 * 15 * 16 * 18 = 60^3, and 5 * 8 * 10 * 15 * 16 * 18 = 120^3.
For n = 19, a(19) = 28 with the sequence 19 XOR 20 XOR 27 XOR 28 = 0. A table illustrating the first eleven terms: n |a(n)| sequence ---+----+------------------- 0 | 0 | 0 1 | 3 | 1 XOR 2 XOR 3 2 | 5 | 2 XOR 3 XOR 4 XOR 5 3 | 6 | 3 XOR 5 XOR 6 4 | 7 | 4 XOR 5 XOR 6 XOR 7 5 | 10 | 5 XOR 6 XOR 9 XOR 10 6 | 9 | 6 XOR 7 XOR 8 XOR 9 7 | 12 | 7 XOR 11 XOR 12 8 | 11 | 8 XOR 9 XOR 10 XOR 11 9 | 14 | 9 XOR 10 XOR 13 XOR 14 10 | 13 | 10 XOR 11 XOR 12 XOR 13
f:= proc(n) local k,S;
S:= {n};
for k from n+1 do
S:= S union map(Bits:-Xor,S,k);
if member(0,S) then return k fi;
od;
end proc:
f(0):= 0:
map(f, [$0..100]); # Robert Israel, Jan 12 2023
f[n_] := Module[{k, S}, S = {n}; For[k = n+1, True, k++, S = S ~Union~ BitXor[S, k]; If[MemberQ[S, 0], Return[k]]]];
f[0] = 0;
f /@ Range[0, 100] (* Jean-François Alcover, Jan 22 2023, after Robert Israel *)
a(n)= if (n==0, return (0), my (x=[n],y); for (m=n+1, oo, if (vecmin(y=[bitxor(v,m) | v<-x])==0, return (m), x=setunion(x,Set(y))))) \\ Rémy Sigrist, Jan 12 2023
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