A162164 Primes p such that p-1 and p+1 can be written as a sum of 2 distinct nonzero squares.

179, 233, 467, 521, 739, 809, 1097, 1171, 1601, 1619, 1801, 1873, 1907, 2467, 3203, 3329, 3331, 3491, 3923, 4051, 4177, 4211, 4931, 5507, 5651, 6067, 6121, 6353, 6569, 6659, 7219, 8081, 8243, 8297, 8353, 8819, 9091, 9161, 9377, 10243, 10531, 10657

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 26 2009

Keywords

• nonn

Examples

			p=179 is a term because 179 - 1 = 3^2 + 13^2 and 179 + 1 = 6^2 + 12^2.
		

Programs

Maple

isA004431 := proc(n) local x,y ; for x from 1 do if x^2 > n then RETURN(false); fi; y := n-x^2 ; if y> 0 and issqr(y ) then y := sqrt(y) ; if y <> x then RETURN(true) ; fi; fi; od: end:
for n from 1 to 2000 do p := ithprime(n) ; if isA004431(p-1) and isA004431(p+1) then printf("%d,",p) ; fi; od: # R. J. Mathar, Jul 02 2009

Mathematica

f[n_]:=Module[{k=1},While[(n-k^2)^(1/2)!=IntegerPart[(n-k^2)^(1/2)],k++; If[2*k^2>=n,k=0;Break[]]];k]; lst={};Do[p=Prime[n];If[f[p-1]>0&&f[p+1]> 0,AppendTo[lst,p]],{n,4*6!}];lst

Formula

{p=A000040(i): p-1 in A004431 and p+1 in A004431}. - R. J. Mathar, Jul 02 2009

Extensions

Definition corrected, R. J. Mathar, Jul 02 2009