A067063 Smallest prime factor of repunit(n) = (10^n-1)/9 (A002275).

11, 3, 11, 41, 3, 239, 11, 3, 11, 21649, 3, 53, 11, 3, 11, 2071723, 3, 1111111111111111111, 11, 3, 11, 11111111111111111111111, 3, 41, 11, 3, 11, 3191, 3, 2791, 11, 3, 11, 41, 3, 2028119, 11, 3, 11, 83, 3, 173, 11, 3, 11, 35121409, 3, 239

Offset: 2

Author

Amarnath Murthy, Jan 03 2002

Keywords

• nonn

Comments

a(n) = A003020(n) = R_(n) iff n is a term of A004023. - Bernard Schott, May 22 2022

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers.

Links

• Ray Chandler, Table of n, a(n) for n = 2..508 (first 499 terms from T. D. Noe - corrected 7 terms)
• Makoto Kamada, Factorizations of 11...11 (Repunit).
• Yousuke Koide, Factorizations of Repunit Numbers
• Amarnath Murthy, On the divisors of Smarandache Unary Sequence, Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000, page 184.
• Samuel S. Wagstaff, the Cunningham Project

Crossrefs

Cf. A002275, A004023, A020639, A102380.

Largest factor: A003020.

Programs

Maple

'min(op(numtheory[factorset]((10^k-1)/9)))'$k=2..50; # M. F. Hasler, Nov 21 2006

Mathematica

a = {}; Do[a = Append[a, FactorInteger[(10^n - 1)/9][[1, 1]]], {n, 2, 111} ]; a
Table[FactorInteger[FromDigits[PadRight[{},n,1]]][[1,1]],{n,2,50}] (* Harvey P. Dale, Dec 10 2013 *)

Formula

a(3n) = 3, a(6n-4) = a(6n-2) = 11, a(30n-25) = a(30n-5) = 41, ... - M. F. Hasler, Nov 21 2006

a(n) = A020639(A002275(n)). - Ray Chandler, Apr 22 2017

Extensions

More terms from Robert G. Wilson v, Jan 04 2002