A138987 a(n) = Frobenius number for 7 successive numbers = F(n+1, n+2, n+3, n+4, n+5, n+6, n+7).

1, 2, 3, 4, 5, 6, 15, 17, 19, 21, 23, 25, 41, 44, 47, 50, 53, 56, 79, 83, 87, 91, 95, 99, 129, 134, 139, 144, 149, 154, 191, 197, 203, 209, 215, 221, 265, 272, 279, 286, 293, 300, 351, 359, 367, 375, 383, 391, 449, 458, 467, 476, 485, 494, 559, 569, 579, 589, 599

Offset: 1

Author

Artur Jasinski, Apr 05 2008

Keywords

• nonn
• easy

Examples

			a(7) = 15 because 15 is the largest number k such that the equation 8*x_1 + 9*x_2 + 10*x_3 + 11*x_4 + 12*x_5 + 13*x_6 + 14*x_7 = k has no solution for any nonnegative x_i (in other words, for every k > 15 there exist one or more solutions).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,2,-2,0,0,0,0,-1,1).

Crossrefs

Frobenius number for k successive numbers: A028387 (k=2), A079326 (k=3), A138984 (k=4), A138985 (k=5), A138986 (k=6), this sequence (k=7), A138988 (k=8).

Programs

Mathematica

Table[FrobeniusNumber[{n+1, n+2, n+3, n+4, n+5, n+6, n+7}], {n, 1, 100}]
Table[FrobeniusNumber[n+Range[7]],{n,100}] (* Harvey P. Dale, Dec 06 2021 *)
Table[n + Floor[(n-1)/6]*(n+1), {n, 100}] (* Giorgos Kalogeropoulos, Apr 06 2025 *)

Formula

G.f.: x*(x^12-7*x^6-x^5-x^4-x^3-x^2-x-1) / ((x-1)^3*(x+1)^2*(x^2-x+1)^2*(x^2+x+1)^2). [Colin Barker, Dec 13 2012]

a(n) = n + (n+1)*floor((n-1)/6). - Giorgos Kalogeropoulos, Apr 06 2025