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

1, 21, 63, 270, 291, 2991, 6102, 46676013, 69460293, 2346534651, 6313047393, 23400000651, 80050617822, 234065340651, 234659934651, 2340000000651, 2530227348360, 2934000006591

Offset: 1

Author

Joseph L. Pe, Apr 11 2002

Keywords

• nonn
• base
• hard
• more

Comments

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

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

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

a(19) > 10^13. - Giovanni Resta, Aug 07 2019

Examples

			phi(291) = 192.
phi(6102) = 2016 = reversal(6102), so 6102 belongs to the sequence.
		

Crossrefs

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

Programs

Mathematica

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

PARI

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

Extensions

More terms from Farideh Firoozbakht, Aug 31 2004

One more term from Farideh Firoozbakht, Jan 09 2005

a(11)-a(13) from Donovan Johnson, Feb 03 2012

a(14)-a(15) from Giovanni Resta, Oct 28 2012

a(16)-a(18) from Giovanni Resta, Aug 07 2019