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

Author

Farideh Firoozbakht, Oct 23 2004

Keywords

• base
• more
• nonn

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

Examples

			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.
		

Links

• Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles & Problems connection.
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A046035, A099077, A099078, A099080.

Programs

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 *)