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A022447
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Fractal sequence of the dispersion of the primes.
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2
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1, 1, 1, 2, 1, 3, 2, 4, 5, 6, 1, 7, 3, 8, 9, 10, 2, 11, 4, 12, 13, 14, 5, 15, 16, 17, 18, 19, 6, 20, 1, 21, 22, 23, 24, 25, 7, 26, 27, 28, 3, 29, 8, 30, 31, 32, 9, 33, 34, 35, 36, 37, 10, 38, 39, 40, 41, 42, 2, 43, 11, 44, 45, 46, 47, 48, 4, 49, 50, 51, 12, 52, 13, 53, 54, 55, 56, 57, 14
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listen;
history;
text;
internal format)
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OFFSET
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1,4
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REFERENCES
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C. Kimberling, Fractal sequences and interspersions, Ars Combinatoria, vol. 45, p. 157, 1997.
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LINKS
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EXAMPLE
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The prime counting function, pi(n), is iterated (possibly zero times) until a nonprime is reached. If the result of this iteration is m, then a(n) = m - pi(m). Examples:
n=11: pi(11)=5, pi(5)=3, pi(3)=2, pi(2)=1. Hence, m=1 and so a(11) = 1-pi(1) = 1.
n=12: is already nonprime, hence m=12 and so a(12) = 12-pi(12) = 7.
n=13: pi(13)=6 (a nonprime), hence m=6 and so a(13) = 6-pi(6) = 3.
(End)
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MATHEMATICA
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m = 30; list = Table[Length[NestWhileList[PrimePi, n, PrimeQ]], {n, m}]; Table[Length@Position[Take[list, k], list[[k]]], {k, Length[list]}] (* Birkas Gyorgy, Apr 04 2011 *)
primefractal[n_]:= (# - PrimePi[#]) &@NestWhile[PrimePi, n, PrimeQ]; Array[primefractal, 30] (* Birkas Gyorgy, Apr 04 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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