A121569 a(n) = Fibonacci((prime(n)+3)/2) - 1.

1, 2, 4, 12, 20, 54, 88, 232, 986, 1596, 6764, 17710, 28656, 75024, 317810, 1346268, 2178308, 9227464, 24157816, 39088168, 165580140, 433494436, 1836311902, 12586269024, 32951280098, 53316291172, 139583862444, 225851433716

Offset: 2

Author

Alexander Adamchuk, Aug 08 2006

Keywords

• nonn

Comments

p = Prime[n] divides a(n) for p = {29,89,101,181,229,349,401,461,509,521,541,709,761,769,809,...} = A047650[n] Primes for which golden mean tau is a quadratic residue or Primes of the form x^2+20y^2.

Crossrefs

Cf. A000045, A121567, A121568, A033205, A045468, A064739, A047650.

Programs

Mathematica

Table[Fibonacci[(Prime[n]+3)/2]-1,{n,2,50}]

Formula

a(n) = Fibonacci[ (Prime[n]+3)/2 ] - 1, n>1. a(n) = Sum[ Fibonacci[k], {k,1,(p-1)/2} ], p = Prime[n], n>1.