

A088165


NSW primes: NSW numbers that are also prime.


34




OFFSET

1,1


COMMENTS

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
Also prime numerators with an odd index in A001333.  Ctibor O. Zizka, Aug 13 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

Table of n, a(n) for n=1..8.
Morris Newman, Daniel Shanks, H. C. Williams, Simple groups of square order and an interesting sequence of primes, Acta Arith., 38 (1980/1981), pp. 129140.
M. Newman, D. Shanks and L. L. Foster, Simple groups of square order (6176), The American Mathematical Monthly, Vol. 86, No. 4 (Apr., 1979), pp. 314315.
The Prime Glossary, NSW numbers


FORMULA

a(n) mod A005850(n) = 1.  Altug Alkan, Mar 17 2016


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

Cf. A002315 (NSW numbers), A005850 (indices for NSW primes).
Sequence in context: A327055 A002315 A141813 * A287810 A292035 A108983
Adjacent sequences: A088162 A088163 A088164 * A088166 A088167 A088168


KEYWORD

nonn


AUTHOR

Christian Schroeder, Sep 21 2003


EXTENSIONS

More terms from Ray Chandler, Sep 21 2003. Next term a(9) is too large (99 digits) to include in sequence.


STATUS

approved



