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Search: id:A069215
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| A069215 |
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Numbers n such that phi(n) = reversal(n). |
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+0 13
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| 1, 21, 63, 270, 291, 2991, 6102, 46676013, 69460293, 2346534651
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Next term is greater than 210000000. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Aug 31 2004
If 10^n-3 is prime (n is in the sequence A089765) and m=3*(10^n-3) then m is in this sequence, for example 299999999999999991 is a term of this sequence because 299999999999999991=3*(10^17-3) and 17 is in the sequence A089675. So 3*(10^A089675-3) is a subsequence of this sequence, A101700 is this subsequence. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Dec 26 2004
A072395 is a subsequence of this sequence. If m is in the sequence and 10 doesn't divide m then reversal(m) is in the sequence A085331, so see Comments on A085331. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Jan 09 2005
If p=(79*10^(4n+1)-83)/101 is prime then 3p is in the sequence. The proof is easy. 21, 2346534651 & 3*(79*10^2697-83)/101 are the first three such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 22 2008, Aug 16 2008
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EXAMPLE
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phi(291) = 192.
phi(6102) = 2016 = reversal(6102), so 6102 belongs to the sequence.
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MATHEMATICA
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Do[If[EulerPhi[n] == FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 1, 10^5}]
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CROSSREFS
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Cf. A069215, A101700.
Cf. A085331, A072395, A101700, A102278.
Sequence in context: A025525 A033850 A113622 this_sequence A115921 A072395 A113781
Adjacent sequences: A069212 A069213 A069214 this_sequence A069216 A069217 A069218
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KEYWORD
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base,nonn,new
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Apr 11 2002
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EXTENSIONS
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More terms from Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Aug 31 2004
One more term from Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Jan 09 2005
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