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A187868 Primes of the form 100^k - 10^k + 1. 1
9901, 99990001, 999999000001, 9999999900000001 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
These primes correspond to k = 2, 4, 6, and 8. There are no other primes of this form for k up to 10000. These primes appear in A187614 because the decimal representation of their reciprocal contains only the digits 0, 1, 8, and 9.
Because these numbers are values of the sixth cyclotomic polynomial, by Theorem 1 of Golomb, the only k that can produce primes are the 3-smooth numbers, 2^i*3^j (A003586).
Next term has k > 1000000. - Robert Gelhar, Aug 20 2020
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 85.
LINKS
Solomon W. Golomb, Cyclotomic polynomials and factorization theorems, Amer. Math. Monthly 85 (1978), 734-737.
MATHEMATICA
Select[Table[100^n - 10^n + 1, {n, 1000}], PrimeQ]
CROSSREFS
Sequence in context: A237917 A205612 A205350 * A072848 A145381 A212401
KEYWORD
nonn,more
AUTHOR
T. D. Noe, Mar 14 2011
STATUS
approved

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Last modified July 21 03:47 EDT 2024. Contains 374463 sequences. (Running on oeis4.)