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

1,1

Links

Table of n, a(n) for n=1..42.

Formula

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

Example

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

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

Crossrefs

Sequence in context: A108384 A217550 A226928 * A238893 A230809 A335067

Adjacent sequences: A162161 A162162 A162163 * A162165 A162166 A162167

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 26 2009

Extensions

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

Status

approved