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A136019
Smallest prime of the form (prime(k)+2*n)/(2*n+1), any k.
56
3, 3, 5, 3, 3, 5, 3, 7, 11, 3, 3, 5, 5, 3, 11, 3, 3, 5, 3, 3, 5, 5, 7, 5, 3, 3, 7, 5, 13, 7, 3, 3, 5, 3, 13, 5, 3, 7, 5, 3, 3, 13, 5, 3, 7, 5, 3, 5, 3, 7, 7, 3, 7, 11, 3, 3, 5, 11, 3, 7, 7, 3, 5, 11, 3, 13, 3, 7, 5, 3, 7, 11, 7, 13, 7, 3, 3, 11, 23, 7, 5, 3, 31, 5, 13, 3, 5, 5, 3, 7, 3, 13, 7, 3, 3, 5, 7
OFFSET
1,1
COMMENTS
The associated prime(k) are in A136020.
LINKS
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