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A065855
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Number of composites <= n.
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50
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0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 18, 19, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 41, 42, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 51, 52, 53
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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COMMENTS
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Also number of primes between prime(n) and n. - Joseph L. Pe, Sep 24 2002
Plot the points (n,a(n)) by, say, appending the line ListPlot[%, PlotJoined -> True] to the Mathematica program. The result is virtually a straight line passing through the origin. For the first thousand points, the slope is approximately = 3/4. (This behavior can be explained by using the prime number theorem.) - Joseph L. Pe, Sep 24 2002
Appears to be the same as the coefficient h*_1 of the h* polynomial for polytope representing the number n. See Ya-Ping Lu and Shu-Fang Deng (2020), Table 3.1. - N. J. A. Sloane, Mar 26 2020
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LINKS
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FORMULA
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EXAMPLE
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Prime(8) = 19 and there are 3 primes between 8 and 19 (endpoints are excluded), namely 11, 13, 17. Hence a(8) = 3.
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MATHEMATICA
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(*gives number of primes < n*) f[n_] := Module[{r, i}, r = 0; i = 1; While[Prime[i] < n, i++ ]; i - 1]; (*gives number of primes between m and n with endpoints excluded*) g[m_, n_] := Module[{r}, r = f[m] - f[n]; If[PrimeQ[n], r = r - 1]; r]; Table[g[Prime[n], n], {n, 1, 1000}]
Accumulate[Table[If[CompositeQ[n], 1, 0], {n, 100}]] (* Harvey P. Dale, Sep 24 2016 *)
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PROG
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(PARI) { for (n=1, 1000, a=n - primepi(n) - 1; write("b065855.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 01 2009
(Haskell)
a065855 n = a065855_list !! (n-1)
a065855_list = scanl1 (+) (map a066247 [1..])
(Python)
from sympy import primepi
return 0 if n < 4 else n - primepi(n) - 1 # Chai Wah Wu, Apr 14 2016
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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STATUS
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approved
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