

A127100


Numbers n such that n^2 divides 10^n1.


30



1, 3, 9, 111, 333, 3003003, 111111111, 225121209, 675363627, 27486820443, 32119664517, 82460461329, 24048075051027, 90180273183093, 225346555330209, 889778776887999, 3336670107774441, 10717272100393839, 19885751580714849, 27514334750263443
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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 from Max Alekseyev, May 09 2010
Edited by Max Alekseyev, May 09 2010


STATUS

approved



