

A072848


Largest prime factor of 10^(6*n) + 1.


1



9901, 99990001, 999999000001, 9999999900000001, 39526741, 3199044596370769, 4458192223320340849, 75118313082913, 59779577156334533866654838281, 100009999999899989999000000010001, 2361000305507449, 111994624258035614290513943330720125433979169
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

According to the link, there are only 18 "unique primes" below 10^50. The first four terms above are each unique primes, of periods 12, 24, 36 and 48, respectively, according to Caldwell and the crossreferenced sequences. These are precisely the only unique primes (less than 10^50 at least) with this type of digit pattern: m 9's, m1 0's and 1, in that order. (Also a(10) is a unique prime of period 120.)


LINKS

Daniel Suteu and Ray Chandler, Table of n, a(n) for n = 1..81 (first 51 terms from Ray Chandler)
C. K. Caldwell, Unique Primes
Makoto Kamada, Factorizations of 100...001.


FORMULA

a(n) = A003021(6n) = A006530(A062397(6n)).  Ray Chandler, May 11 2017


EXAMPLE

10^(6*4)+1 = 17 * 5882353 * 9999999900000001, so a(4) = 9999999900000001, the largest prime factor.


PROG

(PARI) for(n=1, 12, v=factor(10^(6*n)+1); print1(v[matsize(v)[1], 1], ", "))


CROSSREFS

Cf. A040017 (unique period primes), A051627 (associated periods).
Cf. A003021, A006530, A062397.
Sequence in context: A205612 A205350 A187868 * A145381 A212401 A252227
Adjacent sequences: A072845 A072846 A072847 * A072849 A072850 A072851


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, Jul 25 2002


STATUS

approved



