A003021 Largest prime factor of 10^n + 1. (Formerly M2007)

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

0,1

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.

Formula

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

Mathematica

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

Prog

(PARI) for(n=0, 1e2, p=factor(10^n+1)[omega(10^n+1), 1]; print1(p, ", ")) \\ Felix Fröhlich, Aug 13 2014
(Magma) [Maximum(PrimeDivisors(10^n+1)): n in [0..40]]; // Vincenzo Librandi, Jul 12 2016

Crossrefs

Cf. A006530, A062397.

Sequence in context: A001271 A038371 A236174 * A097463 A263607 A083394

Adjacent sequences: A003018 A003019 A003020 * A003022 A003023 A003024

Keyword

nonn,easy

Author

N. J. A. Sloane

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

Status

approved