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Numbers n such that phi(n)=2*reversal(n).
3

%I #14 Aug 13 2019 07:22:42

%S 6180,27630,2914830,4471740,27000630,637062480,27000000630,

%T 679410757980,4412687534631,4421625783741

%N Numbers n such that phi(n)=2*reversal(n).

%C If m>1 and p=3*10^m+7 is prime then 90*p is in the sequence because phi(90*p)=phi(90)*phi(p)=24*(3*10^m+6)=2*(36*10^m+72) =2*reversal(27*10^m+63)=2*reversal(9*p)=2*reversal(90*p). Note that 30 divides all known terms of this sequence. Next term is greater than 11*10^7.

%C a(11) > 10^13. - _Giovanni Resta_, Aug 12 2019

%e 637062480 is a term because phi(637062480) = 2*84260736 = 2*reversal(637062480).

%t Do[If[EulerPhi[n]==2*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 110000000}]

%Y Cf. A000010, A004086, A069215, A114930, A136539, A114931, A136538.

%K nonn,base,more

%O 1,1

%A _Farideh Firoozbakht_, Jan 29 2006

%E a(6)-a(8) from _Giovanni Resta_, Oct 28 2012

%E a(9)-a(10) from _Giovanni Resta_, Aug 12 2019