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

1,1

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)

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Legendre's Conjecture.

Formula

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

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

Example

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

Mathematica

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

Prog

(PARI) { forprime(p=2, 200, f = floor(sqrt(p)) ; print1(2*f+1, ", ") ; ) ; } \\ R. J. Mathar, Apr 21 2006
(Haskell)
a117767 = (+ 1) . (* 2) . a000006  -- Reinhard Zumkeller, Sep 20 2014

Crossrefs

Cf. A000040, A000006.

Cf. A096494, A247485, A247514, A247515.

Sequence in context: A133909 A177691 A206913 * A340836 A293701 A296063

Adjacent sequences: A117764 A117765 A117766 * A117768 A117769 A117770

Keyword

easy,nonn

Author

Odimar Fabeny, Apr 15 2006

Extensions

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

Edited by Dean Hickerson, Jun 03 2006

Status

approved