login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115926 Numbers n such that phi(n)=reversal(n)-n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
EXAMPLE
If n=37, phi(37)= 36 = 73-37
MATHEMATICA
Do[If[EulerPhi[n]==FromDigits[Reverse[IntegerDigits[n]]]-n, Print[n]], {n, 125000000}]
Do[If[EulerPhi[n]==FromDigits[Reverse[IntegerDigits[n]]]-n, Print[n]], {n, 600000000}] - Jessica M. Cornwall (jmc510(AT)psu.edu), Apr 05 2006
CROSSREFS
Cf. A072393.
Sequence in context: A349742 A264626 A201789 * A083818 A090023 A254682
KEYWORD
more,nonn,base
AUTHOR
Farideh Firoozbakht, Jan 31 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
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 05:36 EST 2024. Contains 370291 sequences. (Running on oeis4.)