A073271 - OEIS

%I #30 Sep 08 2022 08:45:06

%S 3,4,7,8,14,14,20,23,24,34,34,38,44,48,52,54,64,64,68,76,76,84,90,92,

%T 98,104,104,110,122,116,132,132,146,140,154,156,160,168,172,174,188,

%U 182,194,194,208,210,214,224,230,234,234,248,246,256,262,264,274,274

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

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

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

%C Conjecture: when a(n) = a(n+1) then A001223(n+1) = A001223(n) + A001223(n+2). - _Gionata Neri_, May 31 2015

%H Harvey P. Dale, <a href="/A073271/b073271.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%t Table[Floor[Prime[n] Prime[n + 2] / Prime[n + 1]], {n, 60}] (* _Vincenzo Librandi_, May 31 2015 *)

%t Floor[(#[[1]]#[[3]])/#[[2]]]&/@Partition[Prime[Range[60]],3,1] (* _Harvey P. Dale_, Jun 07 2021 *)

%o (PARI) vector(100, n, (prime(n)*prime(n+2))\prime(n+1)) \\ _Michel Marcus_, May 31 2015

%o (Magma) [Floor(NthPrime(n)*NthPrime(n+2) / NthPrime(n+1)): n in [1..60]]; // _Vincenzo Librandi_, May 31 2015

%Y Cf. A000040, A022462, A073272, A073273.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 22 2002