A237687 Primes p with pi(p), pi(pi(p)) and pi(p^2) all prime, where pi(.) is given by A000720.

59, 127, 709, 1153, 1787, 9319, 13709, 19577, 32797, 35023, 39239, 40819, 53353, 62921, 75269, 90023, 161159, 191551, 218233, 228451, 235891, 238339, 239087, 272999, 289213, 291619, 339601, 439357, 500741, 513683

Offset

1,1

Comments

This is a subsequence of A237659.

Conjecture: The sequence has infinitely many terms.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000 (n = 1..150 from Zhi-Wei Sun)

Example

a(1) = 59 with 59, pi(59) = 17, pi(pi(59)) = pi(17) = 7 and pi(59^2) = 487 all prime.

Mathematica

p[m_]:=PrimeQ[PrimePi[m^2]]
n=0; Do[If[p[Prime[Prime[Prime[k]]]], n=n+1; Print[n, " ", Prime[Prime[Prime[k]]]]], {k, 1, 1000}]

Crossrefs

Cf. A000040, A000290, A000720, A006450, A038107, A038580, A237656, A237657, A237658, A237659.

Sequence in context: A044627 A050230 A138633 * A098032 A139994 A107157

Adjacent sequences: A237684 A237685 A237686 * A237688 A237689 A237690

Keyword

nonn

Author

Zhi-Wei Sun, Feb 11 2014

Status

approved