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A057855 Greatest k such that (k-th prime) <= (n times n-th prime). 5
1, 3, 6, 9, 16, 21, 30, 36, 46, 61, 68, 86, 99, 110, 126, 146, 168, 184, 205, 223, 242, 270, 292, 321, 360, 381, 404, 429, 446, 477, 546, 574, 614, 637, 693, 717, 762, 804, 842, 890, 935, 965, 1029, 1059, 1105, 1134, 1222, 1304, 1348, 1381, 1423, 1483 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Michel Marcus, Table of n, a(n) for n = 1..5000

FORMULA

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

EXAMPLE

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.

MAPLE

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

seq(a(n), n=1..61);  # Alois P. Heinz, Aug 30 2019

MATHEMATICA

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

PROG

(PARI) a(n) = primepi(n*prime(n)); \\ Michel Marcus, Aug 30 2019

CROSSREFS

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

Sequence in context: A002597 A287554 A308777 * A198685 A070120 A070126

Adjacent sequences:  A057852 A057853 A057854 * A057856 A057857 A057858

KEYWORD

nonn

AUTHOR

Henry Bottomley, Nov 13 2000

STATUS

approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)