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 A065855 Number of composites <= n. 45
 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)
 OFFSET 1,6 COMMENTS 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 Partial sums of A066247, the characteristic function of composites. - Reinhard Zumkeller, Oct 14 2014 LINKS T. D. Noe, Table of n, a(n) for n=1..1000 FORMULA a(n) = n - A000720(n) - 1 = A062298(n) - 1. EXAMPLE Prime(8) = 19 and there are 3 primes between 8 and 19 (endpoints are excluded), namely 11, 13, 17. Hence a(8) = 3. MATHEMATICA (*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}] Table[n-PrimePi[n]-1, {n, 75}] (* Harvey P. Dale, Jun 14 2011 *) Accumulate[Table[If[CompositeQ[n], 1, 0], {n, 100}]] (* Harvey P. Dale, Sep 24 2016 *) PROG (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..]) -- Reinhard Zumkeller, Oct 20 2014 (Python) from sympy import primepi def A065855(n):     return 0 if n < 4 else n - primepi(n) - 1 # Chai Wah Wu, Apr 14 2016 CROSSREFS Cf. A000720, A062298, A002808. Cf. A066247. Sequence in context: A057062 A283993 A255572 * A236863 A242976 A218445 Adjacent sequences:  A065852 A065853 A065854 * A065856 A065857 A065858 KEYWORD easy,nonn,nice AUTHOR Labos Elemer, Nov 26 2001 STATUS approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)