A089452 a(n) = smallest prime k such that k*(prime(n)-1) + prime(n) is prime.

2, 2, 2, 2, 2, 5, 3, 2, 3, 5, 2, 5, 2, 2, 2, 3, 2, 2, 2, 5, 3, 113, 3, 5, 3, 2, 29, 3, 2, 2, 3, 2, 5, 3, 3, 5, 2, 2, 5, 5, 2, 2, 2, 17, 11, 2, 7, 11, 19, 3, 3, 13, 2, 2, 2, 5, 2, 2, 11, 3, 2, 2, 5, 2, 11, 2, 2, 2, 5, 3, 3, 19, 2, 5, 5, 3, 5, 2, 19, 29, 5, 2

Offset

2,1

Comments

Does every prime appear in this sequence? - Gabriel Cunningham (gcasey(AT)mit.edu), Mar 27 2004

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Example

a(2)=2 because 2*(prime(2)-1) + prime(2) = 7, which is prime.
a(7)=5 because 2*(prime(7)-1) + prime(7) = 49 and 3*(prime(7)-1) + prime(7) = 65, both of which are composite, but 5*(prime(7)-1) + prime(7) = 97, which is prime.

Mathematica

spk[n_]:=Module[{k=2}, While[!PrimeQ[k(n-1)+n], k=NextPrime[k]]; k]; spk/@Prime[Range[2, 110]] (* Harvey P. Dale, Nov 06 2014 *)

Prog

(PARI) a(n) = p = prime(n); forprime(k=2, , if (isprime(k*(p-1) + p), return(k); )); \\ Michel Marcus, Nov 18 2014

Crossrefs

Sequence in context: A180214 A329438 A263342 * A162487 A215924 A115101

Adjacent sequences: A089449 A089450 A089451 * A089453 A089454 A089455

Keyword

easy,nonn

Author

Cino Hilliard, Dec 28 2003

Extensions

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Mar 27 2004

Corrected and offset corrected by Harvey P. Dale, Nov 06 2014

Status

approved