A229990 Numbers k such that the interval [floor((k+1)/2), floor(3*(k+1)/2)] contains more primes than the interval [floor(k/2), floor(3*k/2)] does.

1, 3, 4, 8, 12, 19, 20, 24, 28, 31, 40, 44, 48, 52, 55, 64, 67, 68, 71, 72, 84, 91, 92, 99, 100, 104, 108, 111, 115, 120, 127, 128, 131, 132, 140, 148, 151, 152, 155, 160, 171, 175, 180, 184, 187, 188, 204, 208, 211, 220, 224, 231, 232, 235, 239, 244, 248, 252

Offset

1,2

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Example

4 is in this sequence because [[5/2], [15/2]] contains the primes 2,3,5,7, while [[4/2], [12/2]] contains the primes 2,3,5.

Maple

with(numtheory): isA229990 := proc(n) return pi(floor(3*(n+1)/2))-pi(floor((n+1)/2)-1) > pi(floor(3*n/2))-pi(floor(n/2)-1): end proc: seq(`if`(isA229990(n), n, NULL), n=1..252); # Nathaniel Johnston, Oct 11 2013

Mathematica

z = 1000; c[n_] := PrimePi[Floor[3 n/2]] - PrimePi[Floor[n/2]-1];
t = Table[c[n], {n, 1, z}];            (* A229989 *)
Flatten[Position[Differences[t], -1]]  (* A076274? *)
Flatten[Position[Differences[t], 1]]   (* A229990 *)

Crossrefs

Cf. A076274, A229989, A056172.

Sequence in context: A077434 A076136 A064188 * A353188 A147620 A195746

Adjacent sequences: A229987 A229988 A229989 * A229991 A229992 A229993

Keyword

nonn

Author

Clark Kimberling, Oct 09 2013

Status

approved