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%I #15 Mar 29 2015 11:46:01
%S 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,
%T 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,
%U 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
%N Smallest prime p such that also p+prime(n)*2 is a prime.
%C If Polignac's conjecture (1849) is correct, the sequence is defined for all n (as is A020483).
%C Also: least k-prime(n) such that k-prime(n) and k+prime(n) are both primes. - _Pierre CAMI_, Aug 27 2004
%H Charles R Greathouse IV, <a href="/A073703/b073703.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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 *)
%o (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
%o (Haskell)
%o a073703 n = head [p | p <- a000040_list, a010051 (p + 2 * a000040 n) == 1]
%o -- _Reinhard Zumkeller_, Oct 29 2013
%Y Cf. A073704, A001747, A000040, A020483.
%Y Cf. A010051.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 04 2002
%E Merged with Pierre CAMI's submission of Aug 2004 - _R. J. Mathar_, Jul 29 2008
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