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A105223 Number of squares between prime(n) and 2*prime(n) inclusive. 1
1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 6, 6, 6, 5, 5, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 9, 10, 10, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

a(n)>=1 because there is always at least one square between p and 2p.

LINKS

Table of n, a(n) for n=1..103.

FORMULA

a(n) = A000196(2*prime(n)) - A000196(prime(n)-1).

EXAMPLE

a(6)=2 because between 13 and 2*13 there are two squares: 4^2 and 5^2.

MATHEMATICA

f[n_] := Floor[Sqrt[n]]; Table[f[2Prime[n]] - f[Prime[n] - 1], {n, 100}]

CROSSREFS

Cf. A000196, A105224.

Sequence in context: A024937 A143977 A115265 * A025859 A031281 A203181

Adjacent sequences:  A105220 A105221 A105222 * A105224 A105225 A105226

KEYWORD

easy,nonn

AUTHOR

Giovanni Teofilatto, Apr 14 2005

EXTENSIONS

Edited and extended by Ray Chandler, Apr 16 2005

STATUS

approved

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)