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A163848 Primes p such that the differences between p and the closest squares surrounding p are primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A107133 A079138 A319135 * 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

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)