A296307 - OEIS

%I #28 Feb 03 2018 13:29:28

%S 1,5,1,11,2,1,19,7,2,1,29,9,3,2,1,41,17,9,3,2,1,55,20,11,4,3,2,1,71,

%T 31,13,11,4,3,2,1,89,35,23,13,5,4,3,2,1,109,49,26,15,13,5,4,3,2,1,131,

%U 54,29,17,15,6,5,4,3,2,1,155,71,43,29,17,15,6,5,4,3

%N Array read by upwards antidiagonals: f(n,k) = (n+1)*ceiling(n/(k-1)) - 1.

%C f(n,k) = (n+1)*ceiling(n/(k-1))-1 is the Frobenius number F(n+1,n+2,...,n+k), k>1. This formula is derived in "Frobenius number for a set of successive numbers".

%C f(n,k) is the greatest number which is not a linear combination of n+1,n+2,...,n+k with nonnegative coefficients.

%C Example: f(2,3) = 5 because 6=2*3, 7=3+4, 8=2*4, 9=3*3, 10=2*3+4 and so on.

%C Special sequences: f(n,2) = A028387(n), f(n,3) = A079326(n+1), f(n,4) = A138984(n), f(n,5) = A138985(n), f(n,6) = A138986(n), f(n,7) = A138987(n), f(n,8) = A138988(n).

%C f(n,k) is a generalization of these sequences.

%H Gerhard Kirchner, <a href="/A296307/b296307.txt">Table of n, a(n) for n = 1..1000</a>

%H Gerhard Kirchner, <a href="/A296307/a296307.pdf">Frobenius number for a set of successive numbers</a>

%H Gerhard Kirchner, <a href="/A296307/a296307.txt">Table of Frobenius numbers</a>

%H Gerhard Kirchner, <a href="/A296307/a296307_1.txt">Table of Frobenius numbers</a>

%e Example:

%e    f(n,2)   f(n,3)   f(n,4)

%e   a(1)= 1   a(3)=1   a(6) =1

%e   a(2)= 5   a(5)=2   a(9) =2

%e   a(4)=11   a(8)=7   a(13)=3

%e More terms in "Table of Frobenius numbers".

%Y Cf. A028387, A079326, A138984, A138985, A138986, A138987, A138988.

%K nonn,tabl

%O 1,2

%A _Gerhard Kirchner_, Dec 10 2017