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Number of primes up to 10^(n/4).
1

%I #40 Sep 06 2024 08:06:15

%S 0,0,2,3,4,7,11,16,25,40,65,102,168,275,446,739,1229,2039,3401,5703,

%T 9592,16144,27293,46243,78498,133551,227647,388683,664579,1138288,

%U 1951957,3351550,5761455,9915892,17082666,29458442,50847534,87842213,151876932,262795354

%N Number of primes up to 10^(n/4).

%H Amiram Eldar, <a href="/A210518/b210518.txt">Table of n, a(n) for n = 0..80</a> (calculated using Kim Walisch's primecount)

%H Kim Walisch, <a href="https://github.com/kimwalisch/primecount">Fast C++ prime counting function implementation (primecount)</a>.

%F a(n) = primepi(10^(n/4)) = A000720(A018072(n)).

%e a(1) = 0 because 10^(1/4) = 1.77828... and there are no primes less than that.

%e a(2) = 2 because sqrt(10) = 3.16228... and there are 2 primes below that.

%e a(3) = 3 because 10^(3/4) = 5.62341... and there are 3 primes below that.

%t Table[PrimePi[10^(n/4)], {n, 0, 39}] (* _Alonso del Arte_, Jan 26 2013 *)

%Y Cf. A000720, A006880, A018072.

%K nonn,hard

%O 0,3

%A _Vladimir Pletser_, Jan 26 2013