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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A133909 A177691 A206913 * A340836 A293701 A296063
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

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Last modified February 26 19:43 EST 2024. Contains 370352 sequences. (Running on oeis4.)