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%I #22 Sep 11 2022 14:26:48
%S 2,3,9,28,30,31,51,127,208
%N Numbers n such that phi(n).phi(n-1). ... .phi(2).phi(1) is prime (dots between numbers mean concatenation).
%C 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.
%C If it exists, a(10) > 10362. - _J.W.L. (Jan) Eerland_, Aug 14 2022
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8. Primes by Listing</a>, The Prime Puzzles & Problems connection.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%e 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.
%t 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 *)
%t 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 *)
%Y Cf. A046035, A099077, A099078, A099080.
%K base,more,nonn
%O 1,1
%A _Farideh Firoozbakht_, Oct 23 2004
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