A073271 a(n) = floor( prime(n)*prime(n+2) / prime(n+1) ).

3, 4, 7, 8, 14, 14, 20, 23, 24, 34, 34, 38, 44, 48, 52, 54, 64, 64, 68, 76, 76, 84, 90, 92, 98, 104, 104, 110, 122, 116, 132, 132, 146, 140, 154, 156, 160, 168, 172, 174, 188, 182, 194, 194, 208, 210, 214, 224, 230, 234, 234, 248, 246, 256, 262, 264, 274, 274

Offset: 1

Author

Reinhard Zumkeller, Jul 22 2002

Keywords

• nonn

Comments

A000040(n) < a(n) < A000040(n+2);

Conjecture: a(n) is even except for a(1)=3, a(3)=7 and a(8)=23 (A073272(n)=0).

Conjecture: when a(n) = a(n+1) then A001223(n+1) = A001223(n) + A001223(n+2). - Gionata Neri, May 31 2015

Examples

			A000040(10)*A000040(12)/A000040(11) = 29*37/31 = 1073/31 = (34*31+19)/31, therefore a(10)=34; A073272(10) = A000040(11)-a(10) = 31-34 = -3.
		

Links

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

Crossrefs

Cf. A000040, A022462, A073272, A073273.

Programs

Magma

[Floor(NthPrime(n)*NthPrime(n+2) / NthPrime(n+1)): n in [1..60]]; // Vincenzo Librandi, May 31 2015

Mathematica

Table[Floor[Prime[n] Prime[n + 2] / Prime[n + 1]], {n, 60}] (* Vincenzo Librandi, May 31 2015 *)
Floor[(#[[1]]#[[3]])/#[[2]]]&/@Partition[Prime[Range[60]],3,1] (* Harvey P. Dale, Jun 07 2021 *)

PARI

vector(100, n, (prime(n)*prime(n+2))\prime(n+1)) \\ Michel Marcus, May 31 2015