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

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

Offset

1,2

Comments

Subsequence of A014950.

First 7 terms are palindromes. a(n) is divisible by 3 for 1<n<10. 3^2 divides a(n) for n = {3,5,6,7,9}. 37 divides a(n) for n = {4,5,7,8,9}. Prime factors of a(n) are {3,37,333667,2028119,...}. Note that a(3)/a(2) = a(5)/a(4) = a(9)/a(8) = 3 and a(7)/a(6) = 37. - Alexander 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]

Links

Table of n, a(n) for n=1..20.

Mathematica

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

Crossrefs

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

Sequence in context: A281070 A261245 A177243 * A177793 A018778 A291704

Adjacent sequences: A127097 A127098 A127099 * A127101 A127102 A127103

Keyword

nonn

Author

Alexander Adamchuk, Jan 05 2007, Jan 07 2006

Extensions

More terms from Ryan Propper, Jan 06 2007

Further terms and edited by Max Alekseyev, May 09 2010

Status

approved