[seqfan] A formula for a permutation

[Eric Angelini]

Hello SeqFans,
Here is S:
a(1)=0; extend S with the smallest
integer a(n) not yet used such that
2*a(n-1)+a(n) is prime.

S=0,2,1,3,5,7,9,11,15,13,17,25,21,19,
23,...
S is of course a permutation of the
odd numbers -- with 0 and 2 in front.

Here is T:
a(1)=0; extend T with the smallest
integer a(n) not yet used such that
3*a(n-1)+a(n) is prime.

T=0,2,1,4,5,8,7,10,11,14,17,16,13,20,
19,22,...

The integers that will never show are
3,6,9,12,15,18,... of course -- the multiples of 3. And so will it be for
any k like 2,3,4,5...oo

We would like to find a seq X that,
in the same "spirit", would be a
permutation of the integers >=0

What about:

a(1)=0; extend X with the smallest
integer a(n) not yet used such that
a(n-1)^2+a(n) is prime.

X=0,2,1,4,3,8,7,10,9,16,13,12,5,6,11,18,
23,26,...

I think we have it.
Best,
É.


à+
É.
Catapulté de mon aPhone