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

3, 4, 6, 6, 90, 4, 6, 30, 6, 180, 6, 12, 30, 18, 12, 48, 60, 90, 24, 30, 18, 120, 12, 510, 10, 60, 36, 12, 60, 12, 12, 30, 12, 12, 30, 120, 24, 48, 18, 48, 690, 1020, 30, 14, 18, 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

Offset: 1

Author

Zak Seidov, Oct 13 2014

Keywords

• nonn

Examples

			a(1)=3 because p=prime(1)=2 and both P=3^2-2=7 and Q=3^2+2=11 are prime;
a(3)=6 because p=5 and both P=31 and Q=41 are prime;
a(10000)=510 because p=104729 and both P=155371 and Q=364829 are prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A108701, A153975, A176681, A176682, A176683, A177833.

Programs

Mathematica

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 *)

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