A115926 Numbers k such that phi(k) = reversal(k)-k.

37, 397, 1853, 15503, 48776, 198683, 200882, 1061361, 3542805, 3564217, 3868867, 3962197, 4438616, 19844683, 198444683, 202195682, 309520655, 431092646, 439419646, 500729929, 535973599, 3566790217, 3963436297, 4149753226, 17296101143, 39560402197

Offset: 1

Author

Farideh Firoozbakht, Jan 31 2006

Keywords

• nonn
• base

Comments

All primes of the form 4*10^n-3 are in the sequence because if 4*10^n-3 is prime then phi(4*10^n-3)=(4*10^n-4) =(8*10^n-7)-(4*10^n-3)=reversal(4*10^n-3)-(4*10^n-3).

Also if n>1 and p=(94*10^n+113)/9 is prime then 19*p is in the sequence (the proof is easy). Next term is greater than 125*10^6.

If p=(1/303)*(232*10^(4n)+71) is prime then 7*p is in the sequence (the proof is easy). The first four such terms happen for n=2, 101, 104 & 444 and numbers of digits of these terms of the sequence are 9, 405, 417 & 1777 respectively. - Farideh Firoozbakht, Jan 02 2008

a(32) > 10^12. - Giovanni Resta, Oct 28 2012

Examples

			If n=37, phi(37) = 36 = 73-37.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..31

Crossrefs

Cf. A072393.

Programs

Mathematica

Do[If[EulerPhi[n]==FromDigits[Reverse[IntegerDigits[n]]]-n, Print[n]], {n, 600000000}] (* Jessica M. Cornwall (jmc510(AT)psu.edu), Apr 05 2006 *)

Extensions

More terms from Jessica M. Cornwall (jmc510(AT)psu.edu), Apr 05 2006

a(22)-a(31) from Giovanni Resta, Oct 28 2012