A099078 -id:A099078 - cp's OEIS frontend

A099077 Numbers k such that pi(1).pi(2) ... pi(k-1).pi(k) is prime (dot between numbers means concatenation).

5, 25, 2232, 4560

Offset: 1

Farideh Firoozbakht, Oct 23 2004

Number of digits of primes corresponding to the four known terms of this sequence are respectively 4,24,6127,13111. Next term is greater than 10250 and the prime corresponding to the next term has more than 32500 digits.

a(5) > 35000. - Michael S. Branicky, Nov 25 2024

			5 is in the sequence because pi(1).pi(2).pi(3).pi(4).pi(5)=1223 is prime.

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

Cf. A000720, A046035, A099078, A099079, A099080.

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

Original entry on oeis.org

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

Offset: 1

Farideh Firoozbakht, Oct 23 2004

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

			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.

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

Cf. A046035, A099077, A099078, A099080.

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 *)

A099080 Numbers k such that sigma(k).sigma(k-1) ... sigma(2).sigma(1) is prime (dot between numbers means concatenation).

Original entry on oeis.org

2, 3, 66, 102

Offset: 1

Farideh Firoozbakht, Oct 23 2004

Numbers of digits of primes corresponding to the four known terms of this sequence are respectively 2, 3, 133, and 232.
A naive heuristic suggests that this sequence is infinite but extremely sparse. - Charles R Greathouse IV, Nov 05 2013
There are no more terms below 10000. - Charles R Greathouse IV, Nov 09 2013
There are no more terms below 20000. - Michael S. Branicky, Nov 25 2024

			3 is in the sequence because sigma(3).sigma(2).sigma(1) = 431 is prime.

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

Cf. A046035, A099077, A099078, A099079.

Module[{nn=110,d},d=DivisorSigma[1,Range[nn]];Select[Range[nn], PrimeQ[ FromDigits[ Flatten[IntegerDigits/@Reverse[Take[d,#]]]]]&]] (* Harvey P. Dale, Jul 25 2016 *)

s="1";for(n=2,1e3,s=Str(sigma(n),s);if(ispseudoprime(eval(s)), print1(n", "))) \\ Charles R Greathouse IV, Nov 05 2013

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A099077 Numbers k such that pi(1).pi(2) ... pi(k-1).pi(k) is prime (dot between numbers means concatenation).

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

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A099080 Numbers k such that sigma(k).sigma(k-1) ... sigma(2).sigma(1) is prime (dot between numbers means concatenation).

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