

A069215


Numbers n such that phi(n) = reversal(n).


13



1, 21, 63, 270, 291, 2991, 6102, 46676013, 69460293, 2346534651, 6313047393, 23400000651, 80050617822, 234065340651, 234659934651, 2340000000651, 2530227348360, 2934000006591
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OFFSET

1,2


COMMENTS

If 10^n3 is prime (n is in the sequence A089765) and m=3*(10^n3) then m is in this sequence, for example 299999999999999991 is a term of this sequence because 299999999999999991=3*(10^173) and 17 is in the sequence A089675. So 3*(10^A0896753) is a subsequence of this sequence, A101700 is this subsequence.  Farideh Firoozbakht, 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, 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*10^269783)/101 are the first three such terms.  Farideh Firoozbakht, Apr 22 2008, Aug 16 2008
a(19) > 10^13.  Giovanni Resta, Aug 07 2019


LINKS

Table of n, a(n) for n=1..18.


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}]


PROG

(PARI) for( n=1, 1e9, A004086(n)==eulerphi(n) & print1(n", "))


CROSSREFS

Cf. A101700, A004086, A000010, A085331, A072395, A101700, A102278.
Sequence in context: A251213 A170930 A113622 * A115921 A251808 A072395
Adjacent sequences: A069212 A069213 A069214 * A069216 A069217 A069218


KEYWORD

nonn,base,hard,more


AUTHOR

Joseph L. Pe, Apr 11 2002


EXTENSIONS

More terms from Farideh Firoozbakht, Aug 31 2004
One more term from Farideh Firoozbakht, Jan 09 2005
a(11)a(13) from Donovan Johnson, Feb 03 2012
a(14)a(15) from Giovanni Resta, Oct 28 2012
a(16)a(18) from Giovanni Resta, Aug 07 2019


STATUS

approved



