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A136020
Smallest prime of the form (2*n+1)*prime(k)-2*n, any k.
58
7, 11, 29, 19, 23, 53, 31, 103, 191, 43, 47, 101, 109, 59, 311, 67, 71, 149, 79, 83, 173, 181, 283, 197, 103, 107, 331, 229, 709, 367, 127, 131, 269, 139, 853, 293, 151, 463, 317, 163, 167, 1021, 349, 179, 547, 373, 191, 389, 199, 607, 619, 211, 643, 1091, 223
OFFSET
1,1
COMMENTS
The associated prime(k) are in A136019.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1)=7 because 7 is smallest prime p such that (p+2)/3 is prime
a(2)=11 because 11 is smallest prime p such that (p+4)/5 is prime
a(3)=29 because 29 is smallest prime p such that (p+6)/7 is prime
MATHEMATICA
a = {}; Do[k = 1; While[ !PrimeQ[(Prime[k] + 2n)/(2n + 1)], k++ ]; AppendTo[a, Prime[k]], {n, 1, 100}]; a
Reap[Do[k = PrimePi[2n+1]; While[ !PrimeQ[((p=Prime[k]) + 2n)/(2n + 1)], k++ ]; Sow[p], {n, 100}]][[2, 1]] (* Zak Seidov, Mar 04 2013 *)
PROG
(PARI) a(n)=my(t); n+=n; forprime(p=2, default(primelimit), if(isprime(t=(n+1)*p-n), return(t))) \\ Charles R Greathouse IV, Feb 13 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Dec 10 2007
EXTENSIONS
Edited by R. J. Mathar, May 17 2009
STATUS
approved