A127100 Numbers k such that k^2 divides 10^k-1.

1, 3, 9, 111, 333, 3003003, 111111111, 225121209, 675363627, 27486820443, 32119664517, 82460461329, 24048075051027, 90180273183093, 225346555330209, 889778776887999, 3336670107774441, 10717272100393839, 19885751580714849, 27514334750263443

Offset: 1

Author

Alexander Adamchuk, Jan 05 2007, Jan 07 2006

Keywords

• nonn

Comments

Subsequence of A014950.

First 7 terms are palindromes. a(n) is divisible by 3 for 1Alexander Adamchuk, Jan 25 2007

Except for 3, also numbers n such that the decimal expansion of 1/n^2 has period n. - Arkadiusz Wesolowski, Mar 13 2012

Crossrefs

Cf. A127101, A127102, A127103, A127104, A127105, A127106, A127107, A127092, A014950.

Programs

Mathematica

Select[Range[20000], IntegerQ[(PowerMod[10, #, #^2 ]-1)/#^2 ]&]

Extensions

More terms from Ryan Propper, Jan 06 2007

Further terms and edited by Max Alekseyev, May 09 2010