A138986 a(n) = Frobenius number for 6 successive numbers = F(n+1, n+2, n+3, n+4, n+5, n+6).

1, 2, 3, 4, 5, 13, 15, 17, 19, 21, 35, 38, 41, 44, 47, 67, 71, 75, 79, 83, 109, 114, 119, 124, 129, 161, 167, 173, 179, 185, 223, 230, 237, 244, 251, 295, 303, 311, 319, 327, 377, 386, 395, 404, 413, 469, 479, 489, 499, 509, 571, 582, 593, 604, 615, 683, 695, 707

Offset: 1

Author

Artur Jasinski, Apr 05 2008

Keywords

• nonn
• easy

Examples

			a(6)=13 because 13 is the largest number k such that the equation 7*x_1 + 8*x_2 + 9*x_3 + 10*x_4 + 11*x_5 + 12*x_6 = k has no solution for any nonnegative x_i (in other words, for every k > 13 there exist one or more solutions).
		

Links

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

Crossrefs

Frobenius number for k successive numbers: A028387 (k=2), A079326 (k=3), A138984 (k=4), A138985 (k=5), this sequence (k=6), A138987 (k=7), A138988 (k=8).

Programs

Mathematica

Table[FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6}], {n, 1, 100}]
Table[FrobeniusNumber[Range[n,n+5]],{n,2,100}] (* Harvey P. Dale, Dec 22 2018 *)
Table[n + Floor[(n-1)/5]*(n+1), {n, 100}] (* Giorgos Kalogeropoulos, Apr 06 2025 *)

Formula

G.f.: x*(x^10-6*x^5-x^4-x^3-x^2-x-1) / ((x-1)^3*(x^4+x^3+x^2+x+1)^2). [Colin Barker, Dec 13 2012]

a(n) = n + (n+1)*floor((n-1)/5). - Giorgos Kalogeropoulos, Apr 06 2025