login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187868 Primes of the form 100^k - 10^k + 1. 1

%I

%S 9901,99990001,999999000001,9999999900000001

%N Primes of the form 100^k - 10^k + 1.

%C 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.

%C 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).

%C Next term has k > 1000000. - _Robert Gelhar_, Aug 20 2020

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 85.

%H Solomon W. Golomb, <a href="http://www.jstor.org/stable/2321679">Cyclotomic polynomials and factorization theorems</a>, Amer. Math. Monthly 85 (1978), 734-737.

%t Select[Table[100^n - 10^n + 1, {n, 1000}], PrimeQ]

%Y Cf. A003586, A168624, A187614.

%K nonn,more

%O 1,1

%A _T. D. Noe_, Mar 14 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 12 23:35 EDT 2021. Contains 343829 sequences. (Running on oeis4.)