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A237658
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Positive integers m with pi(m) and pi(m^2) both prime, where pi(.) is given by A000720.
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4
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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
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OFFSET
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1,1
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COMMENTS
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The conjecture in A237657 implies that this sequence has infinitely many terms.
For primes in this sequence, see A237659.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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p[m_]:=PrimeQ[PrimePi[m]]&&PrimeQ[PrimePi[m^2]]
n=0; Do[If[p[m], n=n+1; Print[n, " ", m]], {m, 1, 1000}]
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PROG
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(PARI) isok(n) = isprime(primepi(n)) && isprime(primepi(n^2)); \\ Michel Marcus, Apr 28 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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