A163848 Primes p such that the differences between p and the closest squares surrounding p are primes.

7, 11, 23, 47, 83, 167, 227, 443, 1223, 1367, 1847, 2027, 3023, 3251, 5039, 5927, 9803, 11447, 13691, 14639, 16127, 21611, 24023, 36479, 44519, 47087, 49727, 50627, 54287, 61007, 64007, 65027, 88211, 90599, 95483, 103043, 104327, 123203, 137639

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

7-4=3, 9-7=2; 11-9=2, 16-11=5; 23-16=7, 25-23=2; ..

Mathematica

Clear[f, lst, p, n]; f[n_]:=IntegerPart[Sqrt[n]]; lst={}; Do[p=Prime[n]; If[PrimeQ[p-f[p]^2]&&PrimeQ[(f[p]+1)^2-p], AppendTo[lst, p]], {n, 8!}]; lst
spQ[n_]:=Module[{lsq=Floor[Sqrt[n]]}, And@@PrimeQ[{n-lsq^2, (lsq+1)^2-n}]]; Select[Prime[Range[140000]], spQ] (* Harvey P. Dale, May 08 2011 *)

Prog

(PARI) forstep(n=3, 1e6, 2, if(isprime(2*n-3)&&isprime(k=n^2-2), print1(k", ")); if(isprime(2*n-1)&&isprime(k=n^2+2), print1(k", ")))

Crossrefs

Sequence in context: A228227 A107133 A079138 * A111671 A213895 A140111

Adjacent sequences: A163845 A163846 A163847 * A163849 A163850 A163851

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 05 2009

Extensions

Program and editing by Charles R Greathouse IV, Nov 02 2009

Status

approved