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

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

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: A360624 A287554 A308777 * A198685 A070120 A070126

Adjacent sequences: A057852 A057853 A057854 * A057856 A057857 A057858

Keyword

nonn

Author

Henry Bottomley, Nov 13 2000

Status

approved