A114930 Numbers n such that phi(n)=2*reversal(n).

6180, 27630, 2914830, 4471740, 27000630, 637062480, 27000000630, 679410757980, 4412687534631, 4421625783741

Offset

1,1

Comments

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.

a(11) > 10^13. - Giovanni Resta, Aug 12 2019

Links

Table of n, a(n) for n=1..10.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A057880 A151967 A214556 * A068757 A278868 A255791

Adjacent sequences: A114927 A114928 A114929 * A114931 A114932 A114933

Keyword

nonn,base,more

Author

Farideh Firoozbakht, Jan 29 2006

Extensions

a(6)-a(8) from Giovanni Resta, Oct 28 2012

a(9)-a(10) from Giovanni Resta, Aug 12 2019

Status

approved