

A073703


Smallest prime p such that also p+prime(n)*2 is a prime.


16



3, 5, 3, 3, 7, 3, 3, 3, 7, 3, 5, 5, 7, 3, 3, 3, 13, 5, 3, 7, 3, 5, 7, 3, 3, 31, 5, 13, 5, 3, 3, 7, 3, 3, 13, 5, 3, 5, 3, 3, 31, 5, 7, 3, 3, 3, 11, 3, 3, 3, 13, 13, 5, 7, 7, 31, 3, 5, 3, 7, 3, 7, 3, 19, 5, 7, 11, 3, 7, 3, 3, 43, 5, 5, 3, 3, 19, 3, 7, 3, 19, 11, 19, 11, 3, 43, 13, 5, 7, 3, 3, 13, 3
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OFFSET

1,1


COMMENTS

If Polignac's conjecture (1849) is correct, the sequence is defined for all n (as is A020483).
Also: least kprime(n) such that kprime(n) and k+prime(n) are both primes.  Pierre CAMI, Aug 27 2004


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

n=5: prime(5)=11; 2+11*2=24, 3+11*2=25 and 5+11*2=27 are not prime, but 7+11*2=29 is prime, therefore a(5)=7.


MATHEMATICA

f[n_] := Block[{k = Prime[n], p = Prime[n]}, While[ !PrimeQ[k  p]  !PrimeQ[k + p], k++ ]; k  p]; Table[ f[n], {n, 95}] (* Robert G. Wilson v, Aug 28 2004 *)


PROG

(PARI) forprime(q=2, 500, forprime(p=2, default(primelimit), if(isprime(2*q+p), print1(p", "); next(2))); error("Not enough precomputed primes")) \\ Charles R Greathouse IV, Aug 21 2011
(Haskell)
a073703 n = head [p  p < a000040_list, a010051 (p + 2 * a000040 n) == 1]
 Reinhard Zumkeller, Oct 29 2013


CROSSREFS

Cf. A073704, A001747, A000040, A020483.
Cf. A010051.
Sequence in context: A124887 A304903 A097524 * A175019 A097519 A133773
Adjacent sequences: A073700 A073701 A073702 * A073704 A073705 A073706


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Aug 04 2002


EXTENSIONS

Merged with Pierre CAMI's submission of Aug 2004  R. J. Mathar, Jul 29 2008


STATUS

approved



