A074927 - OEIS

%I #17 Dec 04 2016 11:13:41

%S 3,1,1,4,1,4,1,4,9,1,9,4,1,4,9,9,1,9,4,1,9,4,9,16,4,1,4,1,4,49,4,9,1,

%T 25,1,9,9,4,9,9,1,25,1,4,1,36,36,4,1,4,9,1,25,9,9,9,1,9,4,1,25,49,4,1,

%U 4,49,9,25,1,4,9,16,9,9,4,9,16,4,16,25,1,25,1,9,4,9,16,4,1,4,36,16,4

%N a(n) such that p(n)*p(n+1)+a(n) is a minimal square.

%C When a(n)=1, p(n) and p(n+1) are twin primes.

%C a(n+1) = A072681(A024675(n)). - _Reinhard Zumkeller_, Mar 04 2009

%H Vincenzo Librandi, <a href="/A074927/b074927.txt">Table of n, a(n) for n = 1..10000</a>

%F For n>1: a(n) = ((p(n+1)-p(n))/2)^2. - _Reinhard Zumkeller_, Oct 22 2002

%e a(154) = 100 because p(154)*p(155) + 100 = 804609 = 897^2.

%t Flatten[{3,Table[((Prime[n+1]-Prime[n])/2)^2,{n,2,100}]}] (* _Vaclav Kotesovec_, Mar 23 2014 *)

%t Join[{3},((#[[2]]-#[[1]])/2)^2&/@Partition[Prime[Range[2,100]],2,1]] (* _Harvey P. Dale_, Dec 04 2016 *)

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 02 2002