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

1,1

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Sequence in context: A138684 A132442 A364082 * A139605 A191780 A098712

Adjacent sequences: A074924 A074925 A074926 * A074928 A074929 A074930

Keyword

nonn

Author

Zak Seidov, Oct 02 2002

Status

approved