

A138999


First differences of Frobenius numbers for 8 successive numbers A138988.


5



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
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OFFSET

1,7


COMMENTS

For first differences of Frobenius numbers for 2 successive numbers see A005843
For first differences of Frobenius numbers for 3 successive numbers see A014682
For first differences of Frobenius numbers for 4 successive numbers see A138995
For first differences of Frobenius numbers for 5 successive numbers see A138996
For first differences of Frobenius numbers for 6 successive numbers see A138997
For first differences of Frobenius numbers for 7 successive numbers see A138998
For first differences of Frobenius numbers for 8 successive numbers see A138999


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.: (1xx^2x^3x^4x^510*x^6+2*x^13)/((x1)^2*(x^6+x^5+x^4+x^3+x^2+x+1)^2).
a(n) = 2*a(n7)  a(n14).
(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

Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994, A138995, A138996, A138997, A138998, A138999.
Sequence in context: A010173 A259712 A136712 * A265994 A201278 A232589
Adjacent sequences: A138996 A138997 A138998 * A139000 A139001 A139002


KEYWORD

nonn


AUTHOR

Artur Jasinski, Apr 05 2008


STATUS

approved



