OFFSET
1,1
COMMENTS
From Luis H. Gallardo, May 27 2022: (Start)
Let r be a root of the trinomial x^p-x-1 in a fixed algebraic closure F of the finite field F_p. Radoux conjectured in 1975 (see References) that a(n) equals the multiplicative order of r in F. The conjecture seems still open.
Moreover, S. Mattarei proved in 2002 that there exists a finite-dimensional non-nilpotent Lie algebra of characteristic p which admits a nonsingular derivation of order a(n) if p is odd and of order 73 if p = 2. (End)
REFERENCES
S. Mattarei, The orders of nonsingular derivations of modular Lie algebras, Isr. J. Math., 132 (2002), 265-275.
T. S. Motzkin, Sorting numbers ...: for a link to an annotated scanned version of this paper see A000262.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.
C. Radoux, Nombres de Bell, modulo p premier, et extensions de degré p de F_p. C.R. Acad. Sci. Paris Ser. A-B, 281(21) (1975) A879-A882.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..26
J. Levine and R. E. Dalton, Minimum periods, modulo p, of first-order Bell exponential integers, Math. Comp., 16 (1962), 416-423.
W. F. Lunnon, P. A. B. Pleasants, and N. M. Stephens, Arithmetic properties of Bell numbers to a composite modulus I, Acta Arithmetica 35 (1979), pp. 1-16. [From N. J. A. Sloane, Feb 07 2009]
P. L. Montgomery, S. Nahm, and S. S. Wagstaff Jr, The period of the Bell numbers modulo a prime, Math. Comp. 79 (2010), 1793-1800.
MAPLE
for i from 1 to 20 do printf(`%d, `, (ithprime(i)^ithprime(i) -1)/(ithprime(i)-1)) od:
MATHEMATICA
Table[(Prime[n]^Prime[n] - 1)/(Prime[n] - 1), {n, 1, 10}]
(#^#-1)/(#-1)&/@Prime[Range[10]] (* Harvey P. Dale, Apr 09 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Jul 10 2000
STATUS
approved