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a(n) = floor(sqrt(prime(n)*prime(n+2))).
5

%I #18 Sep 08 2022 08:45:06

%S 3,4,7,9,13,15,19,23,26,32,35,39,43,47,52,56,62,65,69,74,77,83,89,94,

%T 99,103,105,109,117,121,131,134,142,144,152,156,161,167,172,176,184,

%U 186,193,195,203,210,218,225,229,233,236,244,248,256,262,266,272,275

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

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

%H Amiram Eldar, <a href="/A073273/b073273.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A098090(A028310(n - 1)) + A089038(n). - _Miko Labalan_, Dec 12 2015

%e prime(10)*prime(12) = 29*37 = 1073 = 32*32+49, therefore a(10)=32; A073274(10) = prime(11)-a(10) = 31-32 = -1.

%t Table[Floor[Sqrt[Prime[n] Prime[n + 2]]], {n, 60}] (* _Vincenzo Librandi_, Dec 12 2015 *)

%o (Magma) [Floor(Sqrt(NthPrime(n)*NthPrime(n+2))): n in [1..60]]; // _Vincenzo Librandi_, Dec 12 2015

%o (PARI) a(n) = sqrtint(prime(n)*prime(n+2)); \\ _Michel Marcus_, Dec 12 2015

%Y Cf. A000040, A073271, A073274, A078444.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 22 2002