%I A088165
%S A088165 7,41,239,9369319,63018038201,489133282872437279,
%T A088165 19175002942688032928599,
%U A088165 123426017006182806728593424683999798008235734137469123231828679
%N A088165 NSW primes: NSW numbers that are also prime.
%C A088165 These primes are the prime RMS numbers (A140480): primes p such that 
               (1+p^2)/2 is a square r^2. Then r is a Pell number, A000129. - T. 
               D. Noe (noe(AT)sspectra.com), Jul 01 2008
%C A088165 Also prime numerators with an odd index in A001333. [From Ctibor O. Zizka 
               (ctibor.zizka(AT)seznam.cz), Aug 13 2008]
%C A088165 r in the above note of T. D. Noe is a prime Pell number (A000129) with 
               an odd index. [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), 
               Aug 13 2008]
%C A088165 General recurrence is a(n)=(a(1)-1)*a(n-1)-a(n-2), a(1)>=4, lim n->infinity 
               a(n)= x*(k*x+1)^n, k =(a(1)-3), x=(1+sqrt((a(1)+1)/(a(1)-3)))/2. 
               Examples in OEIS: a(1)=4 gives A002878, primes in it A121534. a(1)=5 
               gives A001834, primes in it A086386. a(1)=6 gives A030221, primes 
               in it not in OEIS {29,139,3191,...}. a(1)=7 gives A002315, primes 
               in it A088165. a(1)=8 gives A033890, primes in it not in OEIS (does 
               there exist any ?). a(1)=9 gives A057080, primes in it not in OEIS 
               {71,34649,16908641,...}. a(1)=10 gives A057081, primes in it not 
               in OEIS {389806471,192097408520951,...}. [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), 
               Sep 02 2008]
%H A088165 Morris Newman, Daniel Shanks, H. C. Williams, <a href="http://matwbn.icm.edu.pl/
               ksiazki/aa/aa38/aa3826.pdf">Simple groups of square order and an 
               interesting sequence of primes</a>, Acta Arith., 38 (1980/1981) 129-150. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2008]
%H A088165 The Prime Glossary, <a href="http://primes.utm.edu/glossary/page.php?sort=NSWNumber">
               NSW numbers</a>
%Y A088165 Cf. A002315 (NSW numbers), A005850 (indices for NSW primes).
%Y A088165 Sequence in context: A140480 A002315 A141813 this_sequence A108983 A115137 
               A036730
%Y A088165 Adjacent sequences: A088162 A088163 A088164 this_sequence A088166 A088167 
               A088168
%K A088165 nonn
%O A088165 1,1
%A A088165 Schneelocke [Christian Schroeder] (sloane-sequences(AT)gl00on.net), Sep 
               21 2003
%E A088165 More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 21 
               2003. Next term a(9) is too large (99 digits) to include in sequence.