1,1

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

Also prime numerators with an odd index in A001333. [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Aug 13 2008]

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]

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]

Morris Newman, Daniel Shanks, H. C. Williams, Simple groups of square order and an interesting sequence of primes, Acta Arith., 38 (1980/1981) 129-150. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2008]

The Prime Glossary, NSW numbers

Cf. A002315 (NSW numbers), A005850 (indices for NSW primes).

Sequence in context: A140480 A002315 A141813 this_sequence A108983 A115137 A036730

Adjacent sequences: A088162 A088163 A088164 this_sequence A088166 A088167 A088168

nonn

Schneelocke [Christian Schroeder] (sloane-sequences(AT)gl00on.net), Sep 21 2003

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.