A003664 - OEIS

%I M1320 #40 Mar 13 2023 03:52:46

%S 2,5,6,9,10,13,17,20,21,24,28,32,35,36,39,43,47,50,51,54,58,62,65,66,

%T 69,73,77,80,81,84,88,92,95,96,99,103,107,110,111,114,118,122,125,126,

%U 129,133,137,140,141,144,148,152,155,156,159,163,167,170,171,174,178,182

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

%D R. K. Guy, "s-Additive sequences", preprint, 1994.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A003664/b003664.txt">Table of n, a(n) for n = 1..1000</a>

%H Steven R. Finch, <a href="http://dx.doi.org/10.2307/2325001">Are 0-Additive Sequences Always Regular?</a>, Am. Math. Monthly 99 (7) (1992) 671-673.

%H R. K. Guy, <a href="/A007300/a007300.pdf">s-Additive sequences</a>, Preprint, 1994. (Annotated scanned copy)

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F The numbers 2, 5, 6, 9, 13 mod 15, plus the number 10. - _Ralf Stephan_, Mar 28 2004

%F 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

%t Sort[Join[{10},Flatten[Table[15*n+{2,5,6,9,13},{n,0,12}]]]] (* _Harvey P. Dale_, Jul 12 2012 *)

%t 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 *)

%o (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

%o (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

%Y Cf. A007300.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, _Mira Bernstein_