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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A065967 A345209 A117986 * A070737 A225647 A135599

Adjacent sequences: A248735 A248736 A248737 * A248739 A248740 A248741

Keyword

nonn

Author

Zak Seidov, Oct 13 2014

Status

approved