A114930 -id:A114930 - cp's OEIS frontend

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

Farideh Firoozbakht, Jan 29 2006

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

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

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

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

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

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

A136538 Numbers n such that reversal(n)=2*phi(n).

Original entry on oeis.org

2, 4, 8, 42, 84, 2763, 4032, 8064, 67314, 86558, 291483, 2700063, 2700000063, 4039603962, 46420566582, 6739054689866

Offset: 1

Farideh Firoozbakht, Jan 04 2008

If m>1 and p=3*10^m+7 is prime then n=9*p is in the sequence (the proof is easy). If n is an even term of the sequence and the largest digit of n is less than 5(3) then 2n is (both numbers 2n & 4n are) in the sequence (the proof is easy).

a(17) > 10^13. - Giovanni Resta, Aug 12 2019

			Reversal(42)=24=2*12=2*phi(42), so 42 is in the sequence. [Example corrected Jan 25 2008]

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

Do[If[FromDigits@Reverse@IntegerDigits@n==2*EulerPhi[n], Print[n]],{n,100000000}]

a(13)-a(15) from Giovanni Resta, Oct 28 2012

a(16) from Giovanni Resta, Aug 12 2019

cp's OEIS Frontend

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

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