A288119 Lexicographically earliest sequence of distinct nonnegative terms such that, for any i and j >= 0, a(i+j) != a(i) + a(j).

1, 0, 2, 3, 5, 4, 8, 7, 6, 10, 9, 11, 12, 14, 13, 17, 16, 15, 19, 18, 20, 21, 23, 22, 26, 25, 24, 28, 27, 29, 30, 32, 31, 35, 34, 33, 37, 36, 38, 39, 41, 40, 44, 43, 42, 46, 45, 47, 48, 50, 49, 53, 52, 51, 55, 54, 56, 57, 59, 58, 62, 61, 60, 64, 63, 65, 66, 68

Offset: 0

Author

Rémy Sigrist, Jun 05 2017

Keywords

• nonn

Comments

If we drop the unicity constraint, then we obtain A059841.

This sequence is a self-inverse permutation of the natural numbers.

a(1+2+2) = a(1) + a(2) + a(2).

Examples

			See Links section.
		

Links

• Rémy Sigrist, First 9 terms, proof of the formula
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A059841.

Programs

Maple

A[0]:= 1: A[1]:= 0: S:= {0,1}:
for n from 2 to 100 do
  Forbid:= S union {seq(A[i]+A[n-i],i=1..floor(n/2))};
  A[n]:= min( {$1..max(Forbid)+1} minus Forbid);
  S:= S union {A[n]};
od:
[seq(A[i],i=0..100)]; # Robert Israel, Jun 13 2017

Formula

a(n+9) = a(n) + 9 for any n >= 0.

G.f.: (1-x+2*x^2+x^3+2*x^4-x^5+4*x^6-x^7-x^8+3*x^9)/((1-x)*(1-x^9)). - Robert Israel, Jun 13 2017