A020900 Greatest k such that k-th prime < twice n-th prime.

2, 3, 4, 6, 8, 9, 11, 12, 14, 16, 18, 21, 22, 23, 24, 27, 30, 30, 32, 34, 34, 37, 38, 40, 44, 46, 46, 47, 47, 48, 54, 55, 58, 59, 62, 62, 65, 66, 67, 68, 71, 72, 75, 76, 77, 78, 82, 86, 87, 88, 90, 91, 92, 95, 97, 99, 99, 100, 101, 102, 103, 106, 112

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			4th prime is 7, twice the 4th prime is 14, the greatest prime < 14 is 13 that is the 6th prime, hence, a(4) = 6. - _Bernard Schott_, Feb 02 2020
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000720 (pi(n)), A100484 (2*prime(n)).

Cf. A020901, A059788, A060265.

Cf. A102820 (first differences).

Programs

Mathematica

PrimePi[NextPrime[#,-1]]&/@(2Prime[Range[70]]) (* Harvey P. Dale, Jul 05 2012 *)

PARI

a(n) = primepi(2*prime(n)); \\ Michel Marcus, Oct 25 2017; Feb 02 2020

Formula

a(n) = A000720(A100484(n)). - Michel Marcus, Feb 02 2020