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A139104
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Numbers whose binary representation shows the distribution of prime numbers up to the n-th prime, using "0" for primes and "1" for nonprime numbers.
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10
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2, 4, 18, 74, 1198, 4794, 76718, 306874, 4909998, 314239934, 1256959738, 80445423294, 1287126772718, 5148507090874, 82376113453998, 5272071261055934, 337412560707579838, 1349650242830319354, 86377615541140438718, 1382041848658247019502, 5528167394632988078010
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OFFSET
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1,1
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COMMENTS
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a(n) is the decimal representation of A139103(n) interpreted as binary number.
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LINKS
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FORMULA
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a(n) = 2^prime(n) - 1 - (1/2)*(n + Sum_{i=1..prime(n)} 2^(prime(n)-i)*pi(i)), where prime(n) = A000040(n) and pi(n) = A000720(n)
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EXAMPLE
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a(4)=74 because 74 written in base 2 is 1001010 and the string "1001010" shows the distribution of prime numbers up to the 4th prime, using "0" for primes and "1" for nonprime numbers.
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MATHEMATICA
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Table[ sum = 0; For[i = 1, i <= Prime[n] , i++, sum = sum*2;
If[! PrimeQ[i], sum++]]; sum, {n, 1, 21}] (* Robert Price, Apr 03 2019 *)
Module[{nn=30, t}, t=Table[If[PrimeQ[n], 0, 1], {n, Prime[nn]}]; Table[ FromDigits[ Take[t, p], 2], {p, Prime[Range[nn]]}]] (* Harvey P. Dale, Jul 15 2019 *)
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PROG
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(PARI) a(n) = fromdigits(vector(prime(n), k, !isprime(k)), 2); \\ Michel Marcus, Apr 04 2019
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CROSSREFS
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Cf. A000040, A018252, A139101, A139102, A139103, A139119, A139120, A139122, A000720, A001348, A121240.
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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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