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A162164 Primes p such that p-1 and p+1 can be written as a sum of 2 distinct nonzero squares. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A142028

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

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Last modified June 25 22:16 EDT 2019. Contains 324358 sequences. (Running on oeis4.)