A003664 a(n) is smallest number larger than a(n-1) and not = a(j) + a(k), j < k. (Formerly M1320)

2, 5, 6, 9, 10, 13, 17, 20, 21, 24, 28, 32, 35, 36, 39, 43, 47, 50, 51, 54, 58, 62, 65, 66, 69, 73, 77, 80, 81, 84, 88, 92, 95, 96, 99, 103, 107, 110, 111, 114, 118, 122, 125, 126, 129, 133, 137, 140, 141, 144, 148, 152, 155, 156, 159, 163, 167, 170, 171, 174, 178, 182

Offset

1,1

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..1000

Steven R. Finch, Are 0-Additive Sequences Always Regular?, Am. Math. Monthly 99 (7) (1992) 671-673.

R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy)

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

The numbers 2, 5, 6, 9, 13 mod 15, plus the number 10. - Ralf Stephan, Mar 28 2004

G.f.: x*(x^10 +2*x^9 -2*x^8 +2*x^7 +x^6 +x^5 +x^4 +3*x^3 +x^2 +3*x +2) / ((x -1)^2*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Jul 09 2014

Mathematica

Sort[Join[{10}, Flatten[Table[15*n+{2, 5, 6, 9, 13}, {n, 0, 12}]]]] (* Harvey P. Dale, Jul 12 2012 *)
CoefficientList[Series[(x^10 + 2*x^9 - 2 x^8 + 2 x^7 + x^6 + x^5 + x^4 + 3 x^3 + x^2 + 3 x + 2)/((x - 1)^2 (x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 10 2014 *)

Prog

(PARI) Vec(x*(x^10+2*x^9-2*x^8+2*x^7+x^6+x^5+x^4+3*x^3+x^2+3*x+2)/((x-1)^2*(x^4+x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Jul 09 2014
(Magma) I:=[2, 5, 6, 9, 10, 13, 17, 20, 21, 24, 28]; [n le 11 select I[n] else Self(n-1)+Self(n-5)-Self(n-6): n in [1..60]]; // Vincenzo Librandi, Jul 10 2014

Crossrefs

Cf. A007300.

Sequence in context: A288552 A187583 A000277 * A065890 A162177 A373226

Adjacent sequences: A003661 A003662 A003663 * A003665 A003666 A003667

Keyword

nonn,easy

Author

N. J. A. Sloane, Mira Bernstein

Status

approved