

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 nth 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
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OFFSET

1,1


COMMENTS

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


LINKS



FORMULA

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)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



