NSW number

NSW stands for Newman, Shanks, and Williams who wrote a paper [NSW1981] in the 1970’s on the integers of the form
S2m+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 Sp 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)


E. Barcucci, S. Brunetti, A. Del Lungo and F. Del Ristoro, "A combinatorial interpretation of the recurrence fn+1=6fn-fn-1," Discrete Math., 190 (1998) 235--240.  MR 99f:05001
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.]
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