A138999 - OEIS

%I #10 Feb 21 2018 16:54:22

%S 1,1,1,1,1,1,10,2,2,2,2,2,2,18,3,3,3,3,3,3,26,4,4,4,4,4,4,34,5,5,5,5,

%T 5,5,42,6,6,6,6,6,6,50,7,7,7,7,7,7,58,8,8,8,8,8,8,66,9,9,9,9,9,9,74,

%U 10,10,10,10,10,10,82,11,11,11,11,11,11,90,12,12,12,12,12,12,98,13,13,13,13

%N First differences of Frobenius numbers for 8 successive numbers A138988.

%C For first differences of Frobenius numbers for 2 successive numbers see A005843

%C For first differences of Frobenius numbers for 3 successive numbers see A014682

%C For first differences of Frobenius numbers for 4 successive numbers see A138995

%C For first differences of Frobenius numbers for 5 successive numbers see A138996

%C For first differences of Frobenius numbers for 6 successive numbers see A138997

%C For first differences of Frobenius numbers for 7 successive numbers see A138998

%C For first differences of Frobenius numbers for 8 successive numbers see A138999

%H Harvey P. Dale, <a href="/A138999/b138999.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A138988(n+1) - A138988(n).

%F From _R. J. Mathar_, Apr 20 2008: (Start)

%F G.f.: -(-1-x-x^2-x^3-x^4-x^5-10*x^6+2*x^13)/((x-1)^2*(x^6+x^5+x^4+x^3+x^2+x+1)^2).

%F a(n) = 2*a(n-7) - a(n-14).

%F (End)

%F a(n) = -(1/7)*mod(n,7)*x(7+mod(n,7))+(1/7)*mod(n,7)*x(mod(n,7))+x(mod(n,7))-(1/7)*n *x(mod(n,7))+(1/7)*n*x(7+mod(n,7)). - _Alexander R. Povolotsky_, Apr 20 2008

%t a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6, n + 7, n + 8}]], {n, 1, 100}]; Differences[a]

%t Differences[Table[FrobeniusNumber[Range[n,n+7]],{n,2,90}]] (* _Harvey P. Dale_, Oct 02 2011 *)

%Y Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994, A138995, A138996, A138997, A138998, A138999.

%K nonn

%O 1,7

%A _Artur Jasinski_, Apr 05 2008