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

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

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• easy

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).
• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 117.

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).

Crossrefs

Cf. A007300.

Programs

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

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(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 *)

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

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