A296307 Array read by upwards antidiagonals: f(n,k) = (n+1)*ceiling(n/(k-1)) - 1.

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

Offset: 1

Author

Gerhard Kirchner, Dec 10 2017

Keywords

• nonn
• tabl

Comments

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".

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

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.

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).

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

Examples

			Example:
   f(n,2)   f(n,3)   f(n,4)
  a(1)= 1   a(3)=1   a(6) =1
  a(2)= 5   a(5)=2   a(9) =2
  a(4)=11   a(8)=7   a(13)=3
More terms in "Table of Frobenius numbers".
		

Links

• Gerhard Kirchner, Table of n, a(n) for n = 1..1000
• Gerhard Kirchner, Frobenius number for a set of successive numbers
• Gerhard Kirchner, Table of Frobenius numbers
• Gerhard Kirchner, Table of Frobenius numbers

Crossrefs

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