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Least prime P such that 3*p(n)*P*(3*p(n)*P+1)-1, 3*p(n)*P*(3*p(n)*P+1)+1,3*p(n)*P*(3*p(n)*P+3)-1,3*p(n)*P*(3*p(n)*P+3)+1 are all primes with p(i) = i-th prime.
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%I #10 Jan 04 2021 23:03:10

%S 3109,14537,5879,79,6203,22307,12569,2749,2647,2767,15061,33713,64693,

%T 420851,12743,125941,119179,640771,171329,75793,58027,7,129341,4409,

%U 10093,18301,21817,7253,58109,4271,86599,211723,7703,238339,90437,136991,13619,1607,4639

%N Least prime P such that 3*p(n)*P*(3*p(n)*P+1)-1, 3*p(n)*P*(3*p(n)*P+1)+1,3*p(n)*P*(3*p(n)*P+3)-1,3*p(n)*P*(3*p(n)*P+3)+1 are all primes with p(i) = i-th prime.

%H Robert Israel, <a href="/A137839/b137839.txt">Table of n, a(n) for n = 1..1000</a>

%p f:= proc(p) local k;

%p k:= 1:

%p do

%p k:= nextprime(k);

%p if isprime(3*p*k*(3*p*k+1)-1) and

%p isprime(3*p*k*(3*p*k+1)+1) and

%p isprime(3*p*k*(3*p*k+3)-1) and

%p isprime(3*p*k*(3*p*k+3)+1) then return k

%p fi

%p od

%p end proc:

%p map(f, [seq(ithprime(i),i=1..50)]); # _Robert Israel_, Jan 04 2021

%K nonn

%O 1,1

%A _Pierre CAMI_, Apr 29 2008

%E Corrected and extended by _D. S. McNeil_, Dec 10 2010