%I #27 Jan 28 2023 12:13:20
%S 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,
%T 107,111,115,149,154,159,164,169,174,179,221,227,233,239,245,251,257,
%U 307,314,321,328,335,342,349,407,415,423,431,439,447,455,521,530,539
%N a(n) is the Frobenius number for 8 successive numbers n+1, n+2, ..., n+8.
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,2,-2,0,0,0,0,0,-1,1).
%F 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
%e a(8)=17 because 17 is the largest number k such that equation:
%e 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).
%t Table[FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6, n + 7, n + 8}], {n, 1, 100}]
%t Table[FrobeniusNumber[n+Range[8]],{n,100}] (* _Harvey P. Dale_, Sep 22 2015 *)
%Y 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).
%K nonn,easy
%O 1,2
%A _Artur Jasinski_, Apr 05 2008