A267896 - OEIS

%I #19 Sep 08 2022 08:46:15

%S 2,3,9,6,15,9,21,39,15,51,39,21,45,75,84,30,96,69,36,114,81,129,186,

%T 99,51,105,54,111,420,129,201,69,360,75,231,240,165,255,264,90,465,96,

%U 195,99,615,651,225,114,231,354,120,615,381,390,399,135,411,279

%N a(n) = (Prime(n+1)^2 - Prime(n)^2) / 8.

%H Robert Israel, <a href="/A267896/b267896.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = A024675(n) * A028334(n) / 2.

%F a(n) = (A000040(n+1)^2 - A000040(n)^2) / 8.

%F a(n) = A069482(n) / 8.

%p seq((ithprime(n+1)^2 - ithprime(n)^2)/8, n=2..100); # _Robert Israel_, Jan 22 2016

%t Rest[Array[(Prime[# + 1]^2 - Prime[#]^2) / 8 &, 60]] (* _Vincenzo Librandi_, Jan 23 2016 *)

%t (#[[2]]-#[[1]])/8&/@Partition[Prime[Range[2,60]]^2,2,1] (* _Harvey P. Dale_, Aug 01 2022 *)

%o (PARI) a(n) = (prime(n+1)^2 - prime(n)^2)/8; \\ _Michel Marcus_, Jan 22 2016

%o (Magma) [(NthPrime(n+1)^2-NthPrime(n)^2) div 8: n in [2..60]]; // _Vincenzo Librandi_, Jan 23 2016

%Y Cf. A069482, A028334, A024675, A000040.

%K nonn

%O 2,1

%A _Franklin T. Adams-Watters_, Jan 22 2016