A147555 -id:A147555 - cp's OEIS frontend

A147556 Largest prime factor of prime(n)-th repunit number.

11, 37, 271, 4649, 513239, 265371653, 5363222357, 1111111111111111111, 11111111111111111111111, 77843839397, 57336415063790604359, 2212394296770203368013, 201763709900322803748657942361

Offset: 1

Farideh Firoozbakht, Dec 26 2008

nonn

The sequence of repunit primes is a subsequence of this sequence.

			Prime(15)=47 and (10^47-1)/9 = 35121409*316362908763458525001406154038726382279, so a(15)=316362908763458525001406154038726382279.

Table of n, a(n) for n = 1..70
Makoto Kamada, Factorizations of 11...11 (Repunit).

Cf. A000040, A002275, A003020, A004022, A006530, A019328, A147555.

Table[FactorInteger[FromDigits[PadRight[{},n,1]]][[-1,1]],{n,Prime[ Range[15]]}] (* Harvey P. Dale, Feb 23 2016 *)

a(n) = A003020(A000040(n)) = A006530(A002275(A000040(n))) = A006530(A019328(A000040(n))). - Ray Chandler, May 11 2017

Edited by Ray Chandler, Apr 06 2011
terms to a(66) in b-file from Ray Chandler, May 11 2017
a(67)-a(70) in b-file from Max Alekseyev, Apr 26 2022

A386519 Index of the smallest prime p such that the number of digits L in the repeating decimal period of 1/p equals the n-th prime.

Original entry on oeis.org

5, 12, 13, 52, 2431, 16, 153888, 27417323062119920, 223378173194137397198, 452, 406, 150886, 23, 40, 2153717, 28, 92971458509, 130, 40998

Offset: 1

Jean-Marc Rebert, Jul 24 2025

In general, for (q,2*5)=1, the length of the period of 1/q is equal to the multiplicative order of 10 modulo q, which is the smallest k such that 10^k == 1 (mod q). It follows that a(n) must be a prime divisor of 10^prime(n)-1. Hence, apart from a(2), we have prime(a(n)) = A147555(n) and a(20) is the index of the prime 241573142393627673576957439049. - Giovanni Resta, Jul 24 2025

			a(1) = 5, since the 5th prime, p = 11, has a repeating decimal period of length L = 2, and 2 = prime(1). There is no smaller prime for which the period length equals the 1st prime.
 n      a(n)         p  L
 1         5        11  2
 2        12        37  3
 3        13        41  5
 4        52       239  7
 5      2431     21649 11
 6        16        53 13
 7    153888   2071723 17

Cf. A072859, A002371, A249330, A147555.

a(8)-a(19) from Giovanni Resta, Jul 24 2025

cp's OEIS Frontend

A147556 Largest prime factor of prime(n)-th repunit number.

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