Search: id:A137270
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%I A137270
%S A137270 3,5,7,13,17,23,47,53,67,73,83,97,107,113,167,193,197,263,293,317,367,
%T A137270 373,383,457,463,467,487,503,557,593,607,643,647,673,677,683,773,787,
%U A137270 797,823,827,857,877,887,947,1033,1063,1087,1103,1187,1193,1223,1303
%N A137270 Primes p such that p^2 - 6 is also prime.
%C A137270 Each of the primes p = 2,3,5,7,13 has the property that the quadratic 
               polynomial phi(x) = x^2 + x - p^2 takes on only prime values for 
               x = 1,2,...,2p-2; each case giving exactly one repetition, in phi(p-1) 
               = -p and phi(p) = p.
%D A137270 F. G. Frobenius, Uber quadratische Formen, die viele Primzahlen darstellen, 
               Sitzungsber. d. Konigl. Acad. d. Wiss. zu Berlin, 1912, 966 - 980.
%F A137270 A000040 INTERSECT A028879. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 16 2008
%e A137270 The (2 x 7 - 2) -1 = 11 primes given by the polynomial x^2 + x - 7^2 
               for x = 1, 2, ..., 2 x 7 - 2 are -47, -43, -37, -29, -19, -7, 7, 
               23, 41, 61, 83, 107.
%p A137270 isA028879 := proc(n) isprime(n^2-6) ; end: isA137270 := proc(n) isprime(n) 
               and isA028879(n) ; end: for i from 1 to 300 do if isA137270(ithprime(i)) 
               then printf("%d, ",ithprime(i)) ; fi ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 16 2008
%t A137270 f[n_]:=n^2-6; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,p]],{n,
               7!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 16 
               2009]
%Y A137270 Cf. A062326.
%Y A137270 Sequence in context: A067567 A163998 A104294 this_sequence A071111 A038929 
               A070806
%Y A137270 Adjacent sequences: A137267 A137268 A137269 this_sequence A137271 A137272 
               A137273
%K A137270 nonn
%O A137270 1,1
%A A137270 Ben de la Rosa and Johan Meyer (meyerjh.sci(AT)ufa.ac.za), Mar 13 2008
%E A137270 Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 16 2008

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