A071126 Length of least repunit which is a multiple of the n-th prime, or 0 if no such multiple exists.

0, 3, 0, 6, 2, 6, 16, 18, 22, 28, 15, 3, 5, 21, 46, 13, 58, 60, 33, 35, 8, 13, 41, 44, 96, 4, 34, 53, 108, 112, 42, 130, 8, 46, 148, 75, 78, 81, 166, 43, 178, 180, 95, 192, 98, 99, 30, 222, 113, 228, 232, 7, 30, 50, 256, 262, 268, 5, 69, 28, 141, 146, 153, 155, 312, 79, 110

Offset: 1

Author

Lekraj Beedassy, May 28 2002

Keywords

• nonn

Comments

If prime(n) = p then a(n) is a divisor of p-1. - Amarnath Murthy, Nov 11 2002

Examples

			The 13th prime, 41, divides the repunit 11111, the smallest among all R(5k) which are multiples of 41.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1000
• P. De Geest, Repunits and Their Factors
• Amarnath Murthy, On the divisors of Smarandache Unary Sequence, Smarandache Notions Journal, Vol. 11, 2000.
• A. A. A. Steward, Factorization of Repunits[up to R(196)]. Cached copy, Sep 25 2000.
• Michael De Vlieger, Records and positions in first 1000 terms of A071126

Crossrefs

Number of 1's in A077573(n).

Cf. A000042. Apart from a(2), identical to A002371.

Programs

Mathematica

Table[Function[p, If[Divisible[10, p], 0, k = {1}; While[! Divisible[ FromDigits@ k, p], AppendTo[k, 1]]; Length@ k]]@ Prime@ n, {n, 67}] (* Michael De Vlieger, May 20 2017 *)

Python

from sympy import prime
from itertools import count
def a(n):
    if n == 1 or n == 3: return 0
    pn = prime(n)
    return next(k for k in count(1) if 10**k//9%pn == 0)
print([a(n) for n in range(1, 68)]) # Michael S. Branicky, Jul 24 2025