A164323 Numbers m such that m = prime(P) + phi(P), where P is the product of the digits of m.

15, 383, 629, 8297

Offset

1,1

Comments

The product of the digits of next term (if it exists) is greater than 2*10^8.

The sequence is finite since prime(P) ~= P*log(P) and phi(P) < P, while n > 10^(log_9(P)) - 1 > P^1.047. - Max Alekseyev, Dec 14 2011

By computation, any further terms must have P > 10^17. By applying the inequalities p_k < k * (log(k) + log(log(k))) and P < 9^(1 + log_10(n/9)) to the defining equation, any further terms must have m < 1.29 * 10^45. - Lucas A. Brown, Jun 20 2023

Links

Table of n, a(n) for n=1..4.

Lucas A. Brown, Python program.

Example

8297 = prime(8*2*9*7) + phi(8*2*9*7), so 8297 is in the sequence.

Mathematica

Do[If[n=Prime[m]+Eulerphi[m]; m==Apply[Times, IntegerDigits[n]], Print[n]],
{m, 200000000}]
pdnQ[n_]:=Module[{p=Times@@IntegerDigits[n]}, If[p>0, n==Prime[p]+ EulerPhi[ p], 0]]; Select[Range[8300], pdnQ] (* Harvey P. Dale, Aug 12 2022 *)

Crossrefs

Cf. A000040, A000010, A007954, A164322, A164324.

Sequence in context: A035274 A324415 A145409 * A374000 A129615 A286139

Adjacent sequences: A164320 A164321 A164322 * A164324 A164325 A164326

Keyword

base,more,nonn,fini

Author

Farideh Firoozbakht, Aug 13 2009

Extensions

Keyword fini added by Max Alekseyev, Dec 14 2011

Status

approved