A001271 Irregular table read by rows: row n lists prime factors of 10^n + 1, with multiplicity.

2, 11, 101, 7, 11, 13, 73, 137, 11, 9091, 101, 9901, 11, 909091, 17, 5882353, 7, 11, 13, 19, 52579, 101, 3541, 27961, 11, 11, 23, 4093, 8779, 73, 137, 99990001, 11, 859, 1058313049, 29, 101, 281, 121499449, 7, 11, 13, 211, 241, 2161, 9091, 353, 449, 641, 1409, 69857

Offset

0,1

Comments

Except for 2, all these primes are in A028416, and all the primes in A028416 appear here. - Davide Rotondo, Aug 12 2023

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.

Links

Ray Chandler, Rows n=0..310, flattened (from Kamada link).

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Brady Haran and Matt Parker, 100000001 is divisible by 17, YouTube Numberphile video, 2025.

Makoto Kamada, Factorizations of 100...001.

S. S. Wagstaff, Jr., The Cunningham Project.

Example

Table begins:
    2;
   11;
  101;
    7,      11, 13;
   73,     137;
   11,    9091;
  101,    9901;
   11,  909091;
   17, 5882353;
  ...

Mathematica

A001271row[n_] := Flatten[Map[ConstantArray[First[#], Last[#]] &, FactorInteger[10^n + 1]]];
Array[A001271row, 20, 0] (* Paolo Xausa, Dec 09 2025 *)

Crossrefs

Cf. A028416, A057934, A062397, A391444.

Sequence in context: A243950 A056732 A157715 * A038371 A236174 A003021

Adjacent sequences: A001268 A001269 A001270 * A001272 A001273 A001274

Keyword

nonn,tabf

Author

N. J. A. Sloane, revised Jul 13 2009

Extensions

Term ordering corrected by Sean A. Irvine, Apr 11 2012

Minor edits to description by Ray Chandler, May 02 2017

Status

approved