%I #13 Oct 26 2015 22:43:41

%S 1,1,2,2,2,2,6,3,8,2,12,3,4,1,2,1,4,3,4,4,6,4,4,1,4,1,4,4,4,1,10,4,2,

%T 6,2,1,2,2,2,3,22,2,10,1,8,10,4,5,6,2,4,2,2,1,2,5,6,2,12,1,4,1,8,3,2,

%U 3,2,11,8,2,2,2,8,3,2,1,4,2,16,4,6,3,6,1,10,1,10,3,18,1

%N Values k in A084697.

%C Is the sequence unbounded? We know that k exists for any n but is the value of k unbounded?

%H Zak Seidov, <a href="/A263455/b263455.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = (A084697(n+1) - A084697(n))/n.

%p a[1]:= 2: a[2]:= 3:b[1]:= 1: b[2]:= 1:

%p for n from 2 to 1000 do

%p if n::odd then delta:= 2*n

%p else delta:= n

%p fi:

%p for q from a[n] + delta by delta while not isprime(q) do od:

%p a[n+1]:= q:

%p b[n]:= (q - a[n])/n;

%p od:

%p seq(b[n],n=1..1000); # _Robert Israel_, Oct 26 2015

%t a=2;Table[k=1;While[!PrimeQ[b=a+k*n],k++];a=b;k,{n,1000}]

%o (PARI) lista(nn) = {a = 2; for (n=1, nn, k=1; while (!isprime(na=a+k*n), k++); print1(k, ", "); a = na;);} \\ _Michel Marcus_, Oct 21 2015

%Y Cf. A084697.

%K nonn

%O 1,3

%A _Zak Seidov_, Oct 18 2015