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A069215 Numbers n such that phi(n) = reversal(n). 13

%I

%S 1,21,63,270,291,2991,6102,46676013,69460293,2346534651,6313047393,

%T 23400000651,80050617822,234065340651,234659934651,2340000000651,

%U 2530227348360,2934000006591

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

%C 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_, Dec 26 2004

%C 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

%C 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_, Apr 22 2008, Aug 16 2008

%C a(19) > 10^13. - _Giovanni Resta_, Aug 07 2019

%e phi(291) = 192.

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

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

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

%Y Cf. A101700, A004086, A000010, A085331, A072395, A101700, A102278.

%K nonn,base,hard,more

%O 1,2

%A _Joseph L. Pe_, Apr 11 2002

%E More terms from _Farideh Firoozbakht_, Aug 31 2004

%E One more term from _Farideh Firoozbakht_, Jan 09 2005

%E a(11)-a(13) from _Donovan Johnson_, Feb 03 2012

%E a(14)-a(15) from _Giovanni Resta_, Oct 28 2012

%E a(16)-a(18) from _Giovanni Resta_, Aug 07 2019

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Last modified September 18 23:30 EDT 2020. Contains 337175 sequences. (Running on oeis4.)