|
Search: id:A062326
|
|
|
| A062326 |
|
Primes p such that p^2-2 is also prime. |
|
+0
11
|
|
| 2, 3, 5, 7, 13, 19, 29, 37, 43, 47, 61, 71, 89, 103, 107, 127, 131, 139, 173, 191, 211, 223, 233, 239, 257, 293, 313, 337, 359, 421, 443, 449, 467, 491, 523, 541, 569, 587, 607, 653, 677, 719, 727, 733, 743, 751, 757, 761, 797, 811, 863, 881, 1013, 1021
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
When p and p^2-2 are both prime, the fundamental solution of the Pell equation x^2 - n*y^2 = 1, for n=p^2-2, is x=p^2-1 and y=p. See A109748 for the case of n and x both prime. - T. D. Noe, May 19 2007
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
|
|
MATHEMATICA
|
f[n_] := n^2 - 2; lst = {}; Do[p = Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 16 2009]
|
|
PROGRAM
|
(MAGMA) [ p: p in PrimesUpTo(1100) | IsPrime(p^2-2) ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 01 2009]
(PARI) { n=0; forprime (p=2, 5*10^5, if (isprime(p^2 - 2), write("b062326.txt", n++, " ", p); if (n==1000, break)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 05 2009]
|
|
CROSSREFS
|
Cf. A049002 (p^2-2).
Sequence in context: A153800 A147791 A072467 this_sequence A066076 A136288 A088091
Adjacent sequences: A062323 A062324 A062325 this_sequence A062327 A062328 A062329
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
Reiner Martin (reinermartin(AT)hotmail.com), Jul 12 2001
|
|
|
Search completed in 0.002 seconds
|
