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A057855 Greatest k such that (k-th prime) <= (n times n-th prime). 5


%S 1,3,6,9,16,21,30,36,46,61,68,86,99,110,126,146,168,184,205,223,242,

%T 270,292,321,360,381,404,429,446,477,546,574,614,637,693,717,762,804,

%U 842,890,935,965,1029,1059,1105,1134,1222,1304,1348,1381,1423,1483

%N Greatest k such that (k-th prime) <= (n times n-th prime).

%C Might be roughly n^2/2 (seems to be marginally more at least for small n).

%H Michel Marcus, <a href="/A057855/b057855.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = pi(n*prime(n)).

%e a(4)=9 since 4th prime is 7, 4*7=28, greatest prime less than or equal to 28 is 23 which is the 9th prime.

%p a:= n-> numtheory[pi](n*ithprime(n)):

%p seq(a(n), n=1..61); # _Alois P. Heinz_, Aug 30 2019

%t Table[PrimePi[w*Prime[w]], {w, 1, 100}]

%o (PARI) a(n) = primepi(n*prime(n)); \\ _Michel Marcus_, Aug 30 2019

%Y Cf. A020900, A020901, A020934-A020940, A033286 (n*prime(n)).

%K nonn

%O 1,2

%A _Henry Bottomley_, Nov 13 2000

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Last modified May 26 00:32 EDT 2020. Contains 334613 sequences. (Running on oeis4.)