

A088165


NSW primes: NSW numbers that are also prime.


34




OFFSET

1,1


COMMENTS

Next term a(9) is too large (99 digits) to include here.  Ray Chandler, Sep 21 2003
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, Jul 01 2008
r in the above note of T. D. Noe is a prime Pell number (A000129) with an odd index.  Ctibor O. Zizka, Aug 13 2008
General recurrence is a(n) = (a(1)1)*a(n1)  a(n2), 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 the 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 the OEIS {29, 139, 3191, ...}. a(1)=7 gives A002315, primes in it A088165. a(1)=8 gives A033890, primes in it not in the OEIS (do there exist any ?). a(1)=9 gives A057080, primes in it not in the OEIS {71, 34649, 16908641, ...}. a(1)=10 gives A057081, primes in it not in the OEIS {389806471, 192097408520951, ...}.  Ctibor O. Zizka, Sep 02 2008


REFERENCES

Paulo Ribenboim, The New Book of Prime Number Records, 3rd edition, SpringerVerlag, New York, 1995, pp. 367369.


LINKS



FORMULA



PROG

(PARI) w=3+quadgen(32); forprime(p=2, 1e3, if(ispseudoprime(t=imag((1+w)*w^p)), print1(t", "))) \\ Charles R Greathouse IV, Apr 29 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



