A138999 First differences of Frobenius numbers for 8 successive numbers A138988.

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, 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, 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

Offset

1,7

Links

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

Formula

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

From R. J. Mathar, Apr 20 2008: (Start)

G.f.: -x*(-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).

a(n) = 2*a(n-7) - a(n-14). (End)

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

Mathematica

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]
Differences[Table[FrobeniusNumber[Range[n, n+7]], {n, 2, 90}]] (* Harvey P. Dale, Oct 02 2011 *)

Crossrefs

For first differences of Frobenius numbers for k successive numbers see: A005843 (k=2), A014682 (k=3), A138995 (k=4), A138996 (k=5), A138997 (k=6), A151898 (k=7), A138999 (k=8).

Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994.

Sequence in context: A259712 A343103 A136712 * A351306 A265994 A201278

Adjacent sequences: A138996 A138997 A138998 * A139000 A139001 A139002

Keyword

nonn,easy

Author

Artur Jasinski, Apr 05 2008

Status

approved