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Search: id:A069215
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A069215 Numbers n such that phi(n) = reversal(n). +0
13
1, 21, 63, 270, 291, 2991, 6102, 46676013, 69460293, 2346534651 (list; graph; listen)
OFFSET

1,2

COMMENT

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

EXAMPLE

phi(291) = 192.

phi(6102) = 2016 = reversal(6102), so 6102 belongs to the sequence.

MATHEMATICA

Do[If[EulerPhi[n] == FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 1, 10^5}]

CROSSREFS

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

KEYWORD

base,nonn,new

AUTHOR

Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Apr 11 2002

EXTENSIONS

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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Last modified September 6 16:04 EDT 2008. Contains 143483 sequences.


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