A074927 a(n) such that p(n)*p(n+1)+a(n) is a minimal square.

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, 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, 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

Offset: 1

Author

Zak Seidov, Oct 02 2002

Keywords

• nonn

Comments

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

a(n+1) = A072681(A024675(n)). - Reinhard Zumkeller, Mar 04 2009

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Flatten[{3,Table[((Prime[n+1]-Prime[n])/2)^2,{n,2,100}]}] (* Vaclav Kotesovec, Mar 23 2014 *)
Join[{3},((#[[2]]-#[[1]])/2)^2&/@Partition[Prime[Range[2,100]],2,1]] (* Harvey P. Dale, Dec 04 2016 *)

Formula

For n>1: a(n) = ((p(n+1)-p(n))/2)^2. - Reinhard Zumkeller, Oct 22 2002