On Sun, Jan 22, 2006 at 10:59:14PM +0100, Christian Goetz wrote:
> Problem:
> A(n+1)=A(n)+B(n)
> B(n+1)=A(n)*B(n)
> A(1)=B(1)=1
>
> Problem 1: General term A (n), B (n) please ask. (dunno what this one means)
Perhaps they ask for an explicit formula for both A(n) and B(n)?
> Problem 2:
> A(1)=1,A(2)=2,A(3)=3,A(4)=5
> A(5)=11,A(6)=41,A(7)=371,A(8)=13901
>
> B(1)=1,B(2)=1,B(3)=2,B(4)=6
> B(5)=30,B(6)=330,B(7)=13530,B(8)=5019630
>
> Prove for 'A (n) * B (n) +1' the fact that it becomes prime.
Maple again:
> [1, 1]; [isprime(%[1] * %[2] + 1)];
[1, 1]
[true]
> [%%[1] + %%[2], %%[1] * %%[2]]; [isprime(%[1] * %[2] + 1)];
[2, 1]
[true]
> [%%[1] + %%[2], %%[1] * %%[2]]; [isprime(%[1] * %[2] + 1)];
[3, 2]
[true]
> [%%[1] + %%[2], %%[1] * %%[2]]; [isprime(%[1] * %[2] + 1)];
[5, 6]
[true]
> [%%[1] + %%[2], %%[1] * %%[2]]; [isprime(%[1] * %[2] + 1)];
[11, 30]
[true]
> [%%[1] + %%[2], %%[1] * %%[2]]; [isprime(%[1] * %[2] + 1)];
[41, 330]
[false]
> [%%[1] + %%[2], %%[1] * %%[2]]; [isprime(%[1] * %[2] + 1)];
[371, 13530]
[true]
> [%%[1] + %%[2], %%[1] * %%[2]]; [isprime(%[1] * %[2] + 1)];
[13901, 5019630]
[false]
It still doesn't hold.
/* Steinar */
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Homepage: http://www.sesse.net/
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