A130001 Numbers n such that phi(n) is the arithmetic mean of n and reversal(n).

1, 95913, 959913, 526108071, 950039541, 95999999913, 534629946141, 950947559613, 3378374216211, 9599999999913

Offset

1,2

Comments

A number of the form 3*(32*10^n-29) is in the sequence iff n>1 and 1/3*(32*10^n-29) is prime (the proof is easy). The first three such terms are 3*(32*10^3-29),3*(32*10^4-29)& 3*(32*10^9-29).

a(11) > 10^13. - Giovanni Resta, Aug 12 2019

Links

Table of n, a(n) for n=1..10.

Example

phi(950039541)=1/2*(950039541+145930059) so 950039541 is in the sequence.

Mathematica

r[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Do[c=r[n]; If[c+n== 2EulerPhi[n], Print[n]], {n, 200000000}]

Crossrefs

Cf. A000010, A004086, A130000.

Sequence in context: A175598 A078518 A234478 * A253747 A253754 A236779

Adjacent sequences: A129998 A129999 A130000 * A130002 A130003 A130004

Keyword

nonn,base,more

Author

Farideh Firoozbakht, Apr 29 2007

Extensions

a(6)-a(8) from Giovanni Resta, Oct 28 2012

a(9)-a(10) from Giovanni Resta, Aug 12 2019

Status

approved