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Least prime p such that p+3*k*(k+1) is prime for all k=0,...,n.
1

%I #12 Apr 06 2015 10:05:52

%S 2,5,5,5,11,11,11,11,11,11,23,23,23,23,23,23,23,23,23,23,23,23

%N Least prime p such that p+3*k*(k+1) is prime for all k=0,...,n.

%C Inspired by the so-called prime-generating polynomials.

%C Since p | 3n(n+1) for n=p-1, one has a(n) > p(n). Otherwise stated, a(p-1) = p (as, e.g., for p=23) is optimal.

%o (PARI) a(n)=forprime(p=1,,for(i=1,n,ispseudoprime(p+3*(i+1)*i)||next(2));return(p))

%Y Cf. A181963, A181969, A181973, A210626, A211773, A212325, ...

%Y Cf. A005846, A056561.

%Y Cf. A256300, A256301.

%K nonn,more

%O 0,1

%A _M. F. Hasler_, Apr 05 2015