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%I #11 Aug 27 2015 10:28:27
%S 0,1,1,1,1,2,2,1,2,3,2,2,4,1,4,3,1,5,2,2,5,4,3,3,4,3,5,6,3,5,3,2,6,5,
%T 5,5,3,2,5,6,3,4,6,2,7,9,2,5,5,3,9,7,1,5,7,5,5,8,2,8,7,3,8,7,5,7,6,3,
%U 6,9,5,9,7,4,6,8,3,8,9,3
%N Number of primes p <= n such that (p-1)*n+1 is prime.
%C Conjecture: a(n) > 0 for all n > 1.
%H Zhi-Wei Sun, <a href="/A261625/b261625.txt">Table of n, a(n) for n = 1..10000</a>
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arXiv:1211.1588 [math.NT], 2012-2015.
%e a(53) = 1 since 3 and (3-1)*53+1 = 107 are both prime.
%t Do[r=0;Do[If[PrimeQ[(Prime[k]-1)n+1],r=r+1],{k,1,PrimePi[n]}];Print[n," ",r];Continue,{n,1,80}]
%o (PARI) a(n) = my(nb=0); forprime(p=2, n, if (isprime((p-1)*n+1), nb++)); nb; \\ _Michel Marcus_, Aug 27 2015
%Y Cf. A000040, A034693, A258803, A258811, A261437.
%K nonn
%O 1,6
%A _Zhi-Wei Sun_, Aug 27 2015
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