The Prime Glossary: NSW number

NSW number
(another Prime Pages' Glossary entries)

Glossary:

Prime Pages:

Top 5000:

NSW stands for Newman, Shanks, and Williams who wrote a paper [NSW1981] in the 1970’s on the integers of the form

S_2m+1 = ((1 + sqrt(2))^2m+1 + (1 - sqrt(2))^2m+1)/2.

This sequence begins: S₁=1, S₃=7, S₅=41, S₇=239, and S₉=1393. (These numbers arise when addressing the question "is there a finite simple group whose order is a square?")

The NSW primes are obviously prime NSW numbers. The first few are S_p where p = 3, 5, 7, 19, 29, 47, 59, 163, 257, 421, 937, 947, 1493, 1901, 6689, 8087, and 9679. (The next is most likely 28753, a probable-prime.)

See Also: FibonacciPrime

Related pages (outside of this work)

A002315 Sloane's Sequence

References:

BBLR1998
E. Barcucci, S. Brunetti, A. Del Lungo and F. Del Ristoro, "A combinatorial interpretation of the recurrence f_n+1=6f_n-f_n-1," Discrete Math., 190 (1998) 235--240. MR 99f:05001
NSW1980
M. Newman, D. Shanks and H. C. Williams, "Simple groups of square order and an interesting sequence of primes.," Acta. Arith., 38:2 (1980/81) 129--140. MR 82b:20022
Ribenboim95 (p. 367-369)
P. Ribenboim, The new book of prime number records, 3rd edition, Springer-Verlag, New York, NY, 1995. pp. xxiv+541, ISBN 0-387-94457-5. MR 96k:11112 [An excellent resource for those with some college mathematics. Basically a Guinness Book of World Records for primes with much of the relevant mathematics. The extensive bibliography is seventy-five pages.]