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A288119
Lexicographically earliest sequence of distinct nonnegative terms such that, for any i and j >= 0, a(i+j) != a(i) + a(j).
2
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
0,3
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).
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
EXAMPLE
See Links section.
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
CROSSREFS
Cf. A059841.
Sequence in context: A127522 A254103 A048673 * A292575 A096070 A075157
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 05 2017
STATUS
approved