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A248738 Least number m such that both m^2 -/+ prime(n) are (positive) primes.

%I A248738 #19 Nov 22 2014 18:41:23
%S A248738 3,4,6,6,90,4,6,30,6,180,6,12,30,18,12,48,60,90,24,30,18,120,12,510,
%T A248738 10,60,36,12,60,12,12,30,12,12,30,120,24,48,18,48,690,1020,30,14,18,
%U A248738 420,180,18,36,540,42,1230,150,870,36,18,330,870,18,30,18,18,18,150,30,18,30,30,60,180,24,30,36
%N A248738 Least number m such that both m^2 -/+ prime(n) are (positive) primes.
%H A248738 Zak Seidov, <a href="/A248738/b248738.txt">Table of n, a(n) for n = 1..10000</a>
%e A248738 a(1)=3 because p=prime(1)=2 and both P=3^2-2=7 and Q=3^2+2=11 are prime;
%e A248738 a(3)=6 because p=5 and both P=31 and Q=41 are prime;
%e A248738 a(10000)=510 because p=104729 and both P=155371 and Q=364829 are prime.
%t A248738 lnm[n_]:=Module[{m=2,pr=Prime[n]},If[m^2-pr<0,m=Ceiling[Sqrt[pr]]];While[ !AllTrue[m^2+{pr,-pr},PrimeQ],m++];m]; Array[lnm,80] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 22 2014 *)
%o A248738 (PARI) a(n) = { p = prime(n); m = sqrtint(p); until( isprime(m^2-p) && isprime(m^2+p), m++); m} \\ _Michel Marcus_, Oct 13 2014
%Y A248738 Cf. A108701, A153975, A176681, A176682, A176683, A177833.
%K A248738 nonn
%O A248738 1,1
%A A248738 _Zak Seidov_, Oct 13 2014