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 A003663 a(n) is smallest number != a(j)+a(k), j
 1, 6, 8, 10, 12, 15, 17, 19, 24, 26, 28, 33, 35, 37, 42, 44, 46, 51, 53, 55, 60, 62, 64, 69, 71, 73, 78, 80, 82, 87, 89, 91, 96, 98, 100, 105, 107, 109, 114, 116, 118, 123, 125, 127, 132, 134, 136, 141, 143, 145, 150, 152, 154, 159, 161, 163, 168, 170, 172, 177, 179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers congruent to {1, 6, 8} mod 9 plus the number 12. REFERENCES R. K. Guy, ``s-Additive sequences,'' preprint, 1994. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 S. R. Finch, Are 0-additive sequences always regular?, Amer. Math. Monthly, 99 (1992), 671-673. R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy) Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA From Chai Wah Wu, Feb 21 2018: (Start) a(n) = a(n-1) + a(n-3) - a(n-4) for n > 9. G.f.: x*(2*x^8 + x^5 - 3*x^4 + x^3 + 2*x^2 + 5*x + 1)/(x^4 - x^3 - x + 1). (End) MATHEMATICA f[s_List, j_Integer] := Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s, {j}]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[ f[#, 2] &, {1, 6}, 65] (* Robert G. Wilson v, Jul 05 2014 *) LinearRecurrence[{1, 0, 1, -1}, {1, 6, 8, 10, 12, 15, 17, 19, 24}, 70] (* Harvey P. Dale, Jul 25 2018 *) PROG (MAGMA) I:=[1, 6, 8, 10, 12, 15, 17, 19, 24]; [n le 9 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Feb 22 2018 CROSSREFS Cf. A199162, A060469, A060470, A060471, A060472. Cf. A003662, A005408, A026471, A026474, A033627, A051039, A051040, A244151. Sequence in context: A026286 A187085 A303580 * A075396 A269135 A092121 Adjacent sequences:  A003660 A003661 A003662 * A003664 A003665 A003666 KEYWORD nonn AUTHOR STATUS approved

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Last modified July 19 12:49 EDT 2019. Contains 325159 sequences. (Running on oeis4.)