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
Keywords
Examples
7-4=3, 9-7=2; 11-9=2, 16-11=5; 23-16=7, 25-23=2; ..
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Programs
-
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 *) -
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",")))
Extensions
Program and editing by Charles R Greathouse IV, Nov 02 2009