OFFSET
1,1
COMMENTS
The associated prime(k) are in A136020.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1)=3 because 3 is smallest prime of the form (p+2)/3; in this case prime(k)=7.
a(2)=3 because 3 is smallest prime of the form (p+4)/5; in this case prime(k)=11.
a(3)=5 because 5 is smallest prime of the form (p+6)/7; in this case prime(k)=29.
MAPLE
N:= 10^5: # to allow prime(k) <= N
Primes:= select(isprime, [2, seq(2*i+1, i=1..floor((N-1)/2))]):
f:= proc(t, n)
local s;
s:= (t+2*n)/(1+2*n);
type(s, integer) and isprime(s)
end proc:
for n from 1 do
p:= ListTools:-SelectFirst(f, Primes, n);
if p = NULL then break fi;
A[n]:= (p+2*n)/(1+2*n);
od:
seq(A[i], i=1..n-1); # Robert Israel, Sep 08 2014
MATHEMATICA
a = {}; Do[k = 1; While[ !PrimeQ[(Prime[k] + 2n)/(2n + 1)], k++ ]; AppendTo[a, (Prime[k] + 2n)/(2n + 1)], {n, 1, 200}]; a
sp[n_]:=Module[{k=1}, While[!PrimeQ[(Prime[k]+2n)/(2n+1)], k++]; (Prime[ k]+2n)/(2n+1)]; Array[sp, 100] (* Harvey P. Dale, May 20 2021 *)
PROG
(PARI) a(n)=my(N=2*n, k=0, t); forprime(p=2, default(primelimit), k++; t=(p+N)/(N+1); if(denominator(t)==1&isprime(t), return(t))) \\ Charles R Greathouse IV, Jun 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Dec 10 2007
EXTENSIONS
Edited by R. J. Mathar, May 17 2009
STATUS
approved