A114931 Numbers n such that phi(n)=4*reversal(n).

10, 20, 40, 50, 80, 210, 420, 630, 711, 831, 840, 2910, 29910, 40320, 80640, 98361, 673140, 865580, 8656341, 466760130, 694602930, 821412711, 23465346510, 40396039620, 63130473930, 234000006510, 464205665820, 2340653406510, 2346599346510

Offset: 1

Author

Farideh Firoozbakht, Jan 29 2006

Keywords

• nonn
• base
• more

Comments

If p=10^m-3 is prime then 30*p is in the sequence because phi(30*p)=phi(30)*phi(p)=8*(10^m-4)=4*(2*10^m-8)=4*reversal (3*10^m-9)=4*reversal(3*p)=4*reversal(30*p). Next term is greater than 55*10^7.

Let f(m,n)=(78*10^(m+3)+210)*(10^(n*(m+4))-1)/(10^(m+4)-1)+7, if p=f(m,n) is prime then 30*p is a term of the sequence. - Jahangeer Kholdi, Nov 13 2013

Also if p=(1/101)*(680*10000^n+27) is prime then 60*p is in the sequence. - Jahangeer Kholdi, Nov 13 2013

a(30) > 10^13. - Giovanni Resta, Aug 12 2019

Examples

			20 is in the sequence because phi(20)=4*2=4*reversal(20).
		

Crossrefs

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

Programs

Mathematica

Do[If[EulerPhi[n]==4*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 550000000}]

Extensions

a(21)-a(27) from Giovanni Resta, Oct 28 2012

a(28)-a(29) from Giovanni Resta, Aug 12 2019