cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

5, 25, 2232, 4560
Offset: 1

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Author

Farideh Firoozbakht, Oct 23 2004

Keywords

Comments

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

Examples

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

Crossrefs

A099078 Numbers k such that pi(k).pi(k-1) ... pi(3).pi(2) is prime (dot between numbers means concatenation).

Original entry on oeis.org

5, 22, 48, 317, 734, 5235, 12377
Offset: 1

Views

Author

Farideh Firoozbakht, Oct 23 2004

Keywords

Comments

Number of digits of primes corresponding to the five known terms of this sequence are respectively 4, 21, 67, 605, 1633.

Examples

			5 is in the sequence because pi(5).pi(4).pi(3).pi(2) = 3221 is prime.
		

Crossrefs

Programs

  • Maple
    r:= 1: v:= 1: Res:= NULL:
    for k from 3 to 6000 do
       if isprime(k) then r:= r+1 fi;
       v:= v + r*10^(1+ilog10(v));
       if isprime(v) then Res:= Res, k fi
    od:
    Res; # Robert Israel, Nov 20 2018
  • Mathematica
    s = ""; Do[s = ToString[PrimePi[n]] <> s; k = ToExpression[s]; If[PrimeQ[k], Print[n]], {n, 2, 5235}] (* Ryan Propper, Aug 30 2005 *)

Extensions

a(6) from Ryan Propper, Aug 30 2005
a(7) from Michael S. Branicky, Apr 29 2023

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

Views

Author

Farideh Firoozbakht, Oct 23 2004

Keywords

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.
		

Crossrefs

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 *)
Showing 1-3 of 3 results.