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A088165 NSW primes: NSW numbers that are also prime. 22
7, 41, 239, 9369319, 63018038201, 489133282872437279, 19175002942688032928599, 123426017006182806728593424683999798008235734137469123231828679 (list; graph; refs; listen; history; text; internal format)
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. [From 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. [From Ctibor O. Zizka, 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, Sep 02 2008]

REFERENCES

Paulo Ribenboim, The New Book of Prime Number Records, 3rd edition, Springer-Verlag, New York, 1995, pp. 367-369.

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) 129-150. [From R. J. Mathar, Jul 31 2008]

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. 314-315.

The Prime Glossary, NSW numbers

CROSSREFS

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

Sequence in context: A140480 A002315 A141813 * A108983 A115137 A036730

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

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Last modified August 21 15:23 EDT 2014. Contains 245856 sequences.