A138985 a(n) = Frobenius number for 5 successive numbers = F(n+1, n+2, n+3, n+4, n+5).

1, 2, 3, 4, 11, 13, 15, 17, 29, 32, 35, 38, 55, 59, 63, 67, 89, 94, 99, 104, 131, 137, 143, 149, 181, 188, 195, 202, 239, 247, 255, 263, 305, 314, 323, 332, 379, 389, 399, 409, 461, 472, 483, 494, 551, 563, 575, 587, 649, 662, 675, 688, 755, 769, 783, 797, 869

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

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

Example

a(5)=11 because 11 is the largest number k such that the equation 6*x_1 + 7*x_2 + 8*x_3 + 9*x_4 + 10*x_5 = k has no solution for any nonnegative x_i (in other words, for every k > 11 there exist one or more solutions).

Mathematica

Table[FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4}], {n, 1, 100}]
Table[(Floor[(n-1)/4]+1)*(n+1)-1, {n, 57}] (* Zak Seidov, Jan 10 2015 *)
FrobeniusNumber/@Partition[Range[2, 70], 5, 1] (* or *) LinearRecurrence[ {1, 0, 0, 2, -2, 0, 0, -1, 1}, {1, 2, 3, 4, 11, 13, 15, 17, 29}, 70] (* Harvey P. Dale, Oct 07 2016 *)

Prog

(PARI)for (n=1, 57, print1((floor((n-1)/4)+1)*(n+1)-1 ", "))\\ Zak Seidov, Jan 10 2015

Crossrefs

Frobenius number for k successive numbers: A028387 (k=2), A079326 (k=3), A138984 (k=4), this sequence (k=5), A138986 (k=6), A138987 (k=7), A138988 (k=8).

Sequence in context: A160914 A326377 A155768 * A184806 A176541 A295721

Adjacent sequences: A138982 A138983 A138984 * A138986 A138987 A138988

Keyword

nonn,easy

Author

Artur Jasinski, Apr 05 2008

Status

approved