OFFSET
1,1
COMMENTS
a(n) is the smallest not yet used odd prime such that (a(1)+...+a(n))/n is prime.
Conjectured to include all odd prime numbers. - David W. Wilson, Nov 23 2012
LINKS
Zak Seidov and Alois P. Heinz, Table of n, a(n) for n = 1..10000
EXAMPLE
(3+7)/2 = 5, (3+7+5+13)/4 = 7.
MAPLE
q:= proc(n) option remember; is(n<3) end:
a:= proc(n) option remember; local k, p;
if n=1 then 3 else for k while q(k) or
irem(s(n-1)+ithprime(k), n, 'p')>0 or not isprime(p)
do od; q(k):= true; ithprime(k) fi
end:
s:= proc(n) option remember; a(n) +`if`(n<2, 0, s(n-1)) end:
seq (a(n), n=1..100); # Alois P. Heinz, Nov 21 2012
MATHEMATICA
a = 3; s = {a}; sm = a; Do[Do[p = Prime[k]; If[FreeQ[s, p] && PrimeQ[(sm + p)/i], sm = sm + p; AppendTo[s, p]; Break[]], {k, 3, 1000000}], {i, 2, 1000}]; s (* Zak Seidov, Nov 21 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Dec 29 2003
EXTENSIONS
Corrected and extended by Ray Chandler, Dec 31 2003
Definition corrected by David W. Wilson, Nov 23 2012
STATUS
approved