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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.
5
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
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
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