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Search: id:A127858
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| A127858 |
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Positive integers n such that r(n^2)=r(n)^2, where r is the cyclic replacement map of the digits d of n in base 12, that is, d->d+1 if d<11 and d->0 if d=11. |
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6
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| 6, 66, 786, 9426, 113106, 1357266, 16287186, 195446226, 2345354706, 28144256466, 337731077586, 4052772931026, 48633275172306, 583599302067666, 7003191624811986, 84038299497743826, 1008459593972925906
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In base 12 the sequence is 6, 56, 556, 5556, 55556, 555556, 5555556, 55555556, 555555556, 5555555556. If r is the cyclic replacement map in base 10, then the only positive integers n with the property that r(n^2)=r(n)^2 appear to be 5, 45 since, for example, r(45^2)=r(2025)=3136=56^2=r(45)^2.
If a(1)=1, a(n)=12*a(n-1)-6; a(2)=12*1-6=6; a(3)=12*6-6=66 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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EXAMPLE
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a(2)=66 since, in base 12, 66=56, r(56)=67 and r(56^2)=r(2630)=3741=67^2.
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CROSSREFS
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Cf. A117755, A127856, A127857, A127859, A127860, A127861.
Sequence in context: A129554 A165229 A127857 this_sequence A004355 A124862 A130977
Adjacent sequences: A127855 A127856 A127857 this_sequence A127859 A127860 A127861
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KEYWORD
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fini,nonn,base,new
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AUTHOR
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Walter A. Kehowski (wkehowski(AT)cox.net), Feb 04 2007
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EXTENSIONS
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More terms a(11)-a(19) Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009
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