A072848 Largest prime factor of 10^(6*n) + 1.

9901, 99990001, 999999000001, 9999999900000001, 39526741, 3199044596370769, 4458192223320340849, 75118313082913, 59779577156334533866654838281, 100009999999899989999000000010001, 2361000305507449, 111994624258035614290513943330720125433979169

Offset: 1

Author

Rick L. Shepherd, Jul 25 2002

Keywords

• nonn

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.)

Examples

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

Links

• Max Alekseyev, Table of n, a(n) for n = 1..87 (terms n=1..51 from Ray Chandler, n=52..81 from Daniel Suteu)
• C. K. Caldwell, Unique Primes
• Makoto Kamada, Factorizations of 100...001.

Crossrefs

Cf. A040017 (unique period primes), A051627 (associated periods).

Cf. A003021, A006530, A062397.

Programs

PARI

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

Formula

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