

A237687


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 ZhiWei 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

ZhiWei Sun, Feb 11 2014


STATUS

approved



