A102380 Irregular triangle read by rows in which row n lists prime factors (with multiplicity) of the repunit (10^n - 1)/9 (A002275(n)).

1, 11, 3, 37, 11, 101, 41, 271, 3, 7, 11, 13, 37, 239, 4649, 11, 73, 101, 137, 3, 3, 37, 333667, 11, 41, 271, 9091, 21649, 513239, 3, 7, 11, 13, 37, 101, 9901, 53, 79, 265371653, 11, 239, 4649, 909091, 3, 31, 37, 41, 271, 2906161, 11, 17, 73, 101

Offset

1,2

Comments

See A003020 for other links and references.

Links

Rows n=1..352, flattened

Makoto Kamada, Factorizations of 11...11 (repunit).

Yousuke Koide, Factorizations of Repunit Numbers

Franz Lemmermeyer, Simerka - Quadratic Forms and Factorization, arXiv:1201.0282 [math.NT], 2011. For the 19th row = [2071723, 5363222357].

Samuel Yates, The Mystique of Repunits, Math. Mag. 51 (1978), 22-28.

Example

First rows:
    1;
   11;
    3,   37;
   11,  101;
   41,  271;
    3,    7, 11, 13, 37;
  239, 4649;
  ...

Maple

[seq( ifactor((10^n-1)/9), n=1..20)];

Crossrefs

Cf. A002275, A067063, A003020, A204845, A204846, A204847, A204848.

Sequence in context: A087100 A298256 A298927 * A204845 A260597 A147555

Adjacent sequences: A102377 A102378 A102379 * A102381 A102382 A102383

Keyword

nonn,tabf

Author

N. J. A. Sloane, Nov 28 2006

Extensions

First 100 rows in b-file from T. D. Noe, Feb 27 2009

Rows n=101..322 in b-file from Ray Chandler, May 01 2017

Rows n=323..352 in b-file from Max Alekseyev, Apr 26 2022

Status

approved