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A237658
Positive integers m with pi(m) and pi(m^2) both prime, where pi(.) is given by A000720.
4
6, 17, 33, 34, 41, 59, 60, 69, 109, 110, 111, 127, 157, 161, 246, 287, 335, 353, 367, 368, 404, 600, 709, 711, 713, 718, 740, 779, 804, 1153, 1162, 1175, 1437, 1472, 1500, 1526, 1527, 1679, 1729, 1742, 1787, 1826, 2028, 2082, 2104, 2223, 2422, 2616, 2649, 2651
OFFSET
1,1
COMMENTS
The conjecture in A237657 implies that this sequence has infinitely many terms.
For primes in this sequence, see A237659.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10001 (n = 1..3000 from Zhi-Wei Sun)
EXAMPLE
a(1) = 6 since pi(6) = 3 and pi(6^2) = 11 are both prime, but none of pi(1) = 0, pi(2) = 1, pi(3^2) = 4, pi(4^2) = 6 and pi(5^2) = 9 is prime.
MATHEMATICA
p[m_]:=PrimeQ[PrimePi[m]]&&PrimeQ[PrimePi[m^2]]
n=0; Do[If[p[m], n=n+1; Print[n, " ", m]], {m, 1, 1000}]
PROG
(PARI) isok(n) = isprime(primepi(n)) && isprime(primepi(n^2)); \\ Michel Marcus, Apr 28 2018
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 10 2014
STATUS
approved