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A127100
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Numbers n such that n^2 divides 10^n-1.
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26
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1, 3, 9, 111, 333, 3003003, 111111111, 225121209, 675363627, 27486820443, 32119664517, 82460461329, 24048075051027, 90180273183093, 225346555330209, 889778776887999, 3336670107774441, 10717272100393839, 19885751580714849, 27514334750263443
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is a subset of A014950(n) = {1, 3, 9, 27, 81, 111, 243, 333, 729, 999, ...} Numbers n such that n divides 10^n-1.
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 (alex(AT)kolmogorov.com), Jan 25 2007
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MATHEMATICA
| Select[Range[20000], IntegerQ[(PowerMod[10, #, #^2 ]-1)/#^2 ]&]
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CROSSREFS
| Cf. A127101, A127102, A127103, A127104, A127105, A127106, A127107, A127092, A014950.
Sequence in context: A053914 A018757 A177243 * A177793 A018778 A082606
Adjacent sequences: A127097 A127098 A127099 * A127101 A127102 A127103
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 05 2007, Jan 07 2006
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Jan 06 2007
Further terms from Max Alekseyev, May 09 2010
Edited by Max Alekseyev (maxale(AT)gmail.com), May 09 2010
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