A138988 a(n) is the Frobenius number for 8 successive numbers n+1, n+2, ..., n+8.

1, 2, 3, 4, 5, 6, 7, 17, 19, 21, 23, 25, 27, 29, 47, 50, 53, 56, 59, 62, 65, 91, 95, 99, 103, 107, 111, 115, 149, 154, 159, 164, 169, 174, 179, 221, 227, 233, 239, 245, 251, 257, 307, 314, 321, 328, 335, 342, 349, 407, 415, 423, 431, 439, 447, 455, 521, 530, 539

Offset

1,2

Links

Table of n, a(n) for n=1..59.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,2,-2,0,0,0,0,0,-1,1).

Formula

G.f.: x*(x^14 - 8*x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1) / ((x-1)^3*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)^2). - Colin Barker, Dec 13 2012

Example

a(8)=17 because 17 is the largest number k such that equation:
9*x_1 + 10*x_2 + 11*x_3 + 12*x_4 + 13*x_5 + 14*x_6 + 15*x_7 + 16*x_8 = k has no solution for any nonnegative x_i (in other words, for every k > 17 there exist one or more solutions).

Mathematica

Table[FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6, n + 7, n + 8}], {n, 1, 100}]
Table[FrobeniusNumber[n+Range[8]], {n, 100}] (* Harvey P. Dale, Sep 22 2015 *)

Crossrefs

Frobenius number for k successive numbers: A028387 (k=2), A079326 (k=3), A138984 (k=4), A138985 (k=5), A138986 (k=6), A138987 (k=7), this sequence (k=8).

Sequence in context: A325829 A171678 A039090 * A055520 A037342 A200333

Adjacent sequences: A138985 A138986 A138987 * A138989 A138990 A138991

Keyword

nonn,easy

Author

Artur Jasinski, Apr 05 2008

Status

approved