A099079 Numbers n such that phi(n).phi(n-1). ... .phi(2).phi(1) is prime (dots between numbers mean concatenation).

2, 3, 9, 28, 30, 31, 51, 127, 208

Offset

1,1

Comments

Number of digits of primes corresponding to the nine known terms of this sequence are respectively 2,3,9,39,42,44,84,244,441.

If it exists, a(10) > 10362. - J.W.L. (Jan) Eerland, Aug 14 2022

If it exists, a(10) > 25000. - Michael S. Branicky, Aug 23 2024

Links

Table of n, a(n) for n=1..9.

Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles & Problems connection.

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Example

9 is in the sequence because phi(9).phi(8).phi(7).phi(6).phi(5).phi(4).phi(3).phi(2).phi(1) = 646242211 is prime.

Mathematica

Module[{nn=210, eph}, eph=EulerPhi[Range[nn]]; Position[Table[FromDigits[ Flatten[ IntegerDigits[Reverse[Take[eph, n]]]]], {n, nn}], _?PrimeQ]]// Flatten (* Harvey P. Dale, Apr 21 2020 *)
ParallelTable[If[PrimeQ[ToExpression[StringJoin[ToString[#]&/@Reverse[Table[EulerPhi[k], {k, 1, n}]]]]], n, Nothing], {n, 1, 10^4}]//.{}->Nothing (* J.W.L. (Jan) Eerland, Aug 15 2022 *)

Crossrefs

Cf. A046035, A099077, A099078, A099080.

Sequence in context: A057248 A015960 A376478 * A339831 A006797 A144239

Adjacent sequences: A099076 A099077 A099078 * A099080 A099081 A099082

Keyword

base,more,nonn

Author

Farideh Firoozbakht, Oct 23 2004

Status

approved