[seqfan] Re: minima of certain sets(recursive)

[Tobias Friedrich]

Hello,

the files should be online, but you can download the files from another destination:
http://gymnasium-pegnitz.de/eigene/testtobi/folge.pdf
http://gymnasium-pegnitz.de/eigene/testtobi/fach.pdf

Morover I assume that you can the simplify calculation of this sequence, since other sequences like the following could be calculated easily.

Eeasy Sequence:
a(n) is the smallest positive integer not occurring 
previously in the sequence, and not representable as 1x_1+K_2*x_2+..+K_q*x_q where x_1,x_2,...,x_q is in the sequence.

The number a appears in the sequence, if and only if a=1,2,... or K_2+...+K_q mod ((1+K_2+...+K_q)*(K_2+...+K_q)).

This sequnces are the reults of the following game:
There are piles with n_1,...,n_k ?tootpicks? and a function F:N^(k+1} -> N.
A player choose a pile with x toothpicks and make k new piles with x_1,...,x_k toothpicks, whereas F(x_1,...,x_k,a)=0. 
The player who cant move loses the game.

Assume F(x_1,x_2,a)=2*x_1+3*x_2-a, then (x_1,x_2) is a winning position if x_1,x_2 is not in the sequence.

Tobias Friedrich 
ify calculation of this sequence, since other sequences like the following could be calculated easily.

Eeasy Sequence:
a(n) is the smallest positive integer not occurring 
previously in the sequence, and not representable as 1x_1+K_2*x_2+..+K_q*x_q where x_1,x_2,...,x_q is in the sequence.

The number a appears in the sequence, if and only if a=1,2,... or K_2+...+K_q mod ((1+K_2+...+K_q)*(K_2+...+K_q)).

This sequnces are the reults of the following game:
There are piles with n_1,...,n_k ?tootpicks? and a function F:N^(k+1} -> N.
A player choose a pile with x toothpicks and make k new pi