A117767 a(n) is the difference between the smallest square greater than prime(n) and the largest square less than prime(n), where prime(n) = A000040(n) is the n-th prime number.

3, 3, 5, 5, 7, 7, 9, 9, 9, 11, 11, 13, 13, 13, 13, 15, 15, 15, 17, 17, 17, 17, 19, 19, 19, 21, 21, 21, 21, 21, 23, 23, 23, 23, 25, 25, 25, 25, 25, 27, 27, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 33, 33, 33, 33, 33, 33, 33, 35, 35, 35, 35, 35, 37, 37, 37, 37, 37, 37

Offset: 1

Author

Odimar Fabeny, Apr 15 2006

Keywords

• easy
• nonn

Comments

From Reinhard Zumkeller, Sep 20 2014: (Start)

a(n) <= floor(2*sqrt(prime(n))) + 1 = A247485(n).

a(A247514(n)) = A247485(A247514(n)).

a(A247515(n)) < A247485(A247515(n)). (End)

Examples

			The 7th prime number is 17, which is between the consecutive squares 16 and 25, so a(7) = 25 - 16 = 9.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Legendre's Conjecture.

Crossrefs

Cf. A000040, A000006.

Cf. A096494, A247485, A247514, A247515.

Programs

Haskell

a117767 = (+ 1) . (* 2) . a000006  -- Reinhard Zumkeller, Sep 20 2014

Mathematica

a[n_]:=2Floor[Sqrt[Prime[n]]]+1

PARI

{ forprime(p=2,200, f = floor(sqrt(p)) ; print1(2*f+1,",") ; ) ; } \\ R. J. Mathar, Apr 21 2006

Formula

a(n) = 2*A000006(n) + 1.

a(n) = 2*floor(sqrt(prime(n))) + 1. - R. J. Mathar, Apr 21 2006

Extensions

More terms from R. J. Mathar, Apr 21 2006

Edited by Dean Hickerson, Jun 03 2006