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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 cross-referenced sequences. These are precisely the only unique primes (less than 10^50 at least) with this type of digit pattern: m 9's, m-1 0's and 1, in that order. (Also a(10) is a unique prime of period 120.)

LINKS

Ray Chandler, Table of n, a(n) for n = 1..51

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

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Last modified May 15 08:59 EDT 2021. Contains 343909 sequences. (Running on oeis4.)