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A163848 Primes p such that the differences between p and the closest squares surrounding p are primes. 2

%I

%S 7,11,23,47,83,167,227,443,1223,1367,1847,2027,3023,3251,5039,5927,

%T 9803,11447,13691,14639,16127,21611,24023,36479,44519,47087,49727,

%U 50627,54287,61007,64007,65027,88211,90599,95483,103043,104327,123203,137639

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

%H G. C. Greubel, <a href="/A163848/b163848.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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

%t 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 *)

%o (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",")))

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Aug 05 2009

%E Program and editing by _Charles R Greathouse IV_, Nov 02 2009

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Last modified January 27 09:09 EST 2020. Contains 331293 sequences. (Running on oeis4.)