A136019 Smallest prime of the form (prime(k)+2*n)/(2*n+1), any k.

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

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

Cf. A136020, A136026, A136027.

Sequence in context: A269733 A138479 A202106 * A242017 A063714 A235649

Adjacent sequences: A136016 A136017 A136018 * A136020 A136021 A136022

Keyword

nonn,easy

Author

Artur Jasinski, Dec 10 2007

Extensions

Edited by R. J. Mathar, May 17 2009

Status

approved