A003021 Largest prime factor of 10^n + 1.

2, 11, 101, 13, 137, 9091, 9901, 909091, 5882353, 52579, 27961, 8779, 99990001, 1058313049, 121499449, 9091, 69857, 21993833369, 999999000001, 909090909090909091, 5964848081, 909091, 1056689261, 549797184491917

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
• Ehrhard Behrends, Five-Minute Mathematics, translated by David Kramer. American Mathematical Society (2008) p. 7.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Table of n, a(n) for n = 0..331
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• T. Granlund, Factors of 10^n + 1.
• Makoto Kamada, Factorizations of 100...001.
• S. S. Wagstaff, Jr., The Cunningham Project.

Crossrefs

Cf. A006530, A062397.

Programs

Magma

[Maximum(PrimeDivisors(10^n+1)): n in [0..40]]; // Vincenzo Librandi, Jul 12 2016

Mathematica

Table[FactorInteger[10^n + 1][[-1, 1]], {n, 0, 29}] (* Alonso del Arte, Oct 21 2011 *)

PARI

for(n=0, 1e2, p=factor(10^n+1)[omega(10^n+1), 1]; print1(p, ", ")) \\ Felix Fröhlich, Aug 13 2014

Formula

a(n) = A006530(A062397(n)). - Vincenzo Librandi, Jul 12 2016

Extensions

More terms from Jason Earls, Jul 11 2001

Terms up to a(280) in b-file from D. S. McNeil, Oct 22 2011

a(281)-a(310) in b-file from Ray Chandler, May 02 2017

a(311)-a(331) in b-file from Max Alekseyev, Apr 24 2019, Feb 13 2020, May 13 2022