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A336404
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a(n) = floor(n*frac(prime(n)/pi(n))), where frac denotes the fractional part.
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1
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0, 1, 2, 3, 2, 1, 6, 6, 2, 2, 4, 10, 2, 12, 13, 7, 12, 7, 17, 2, 19, 5, 21, 19, 5, 12, 24, 26, 9, 16, 29, 15, 21, 19, 26, 3, 22, 35, 16, 31, 38, 27, 34, 3, 9, 3, 41, 6, 13, 27, 48, 3, 37, 3, 24, 46, 54, 17, 31, 44, 17, 3, 17
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OFFSET
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2,3
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COMMENTS
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Conjecture: For any m >= 0 there is a k such that a(k) = m. Also for any reals x and epsilon such that 0 < x < 1 and epsilon > 0, there is a k such that abs(x - frac(prime(k)/pi(k))) < epsilon.
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LINKS
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MATHEMATICA
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a[n_] := Floor[n*FractionalPart[Prime[n]/PrimePi[n]]]; Table[a[n], {n, 2, 2^6}]
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PROG
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(PARI) a(n) = floor(n*frac(prime(n)/primepi(n))); \\ Michel Marcus, Jul 21 2020
(PARI) first(n) = {my(t = 2, res = vector(n), pit = 0); forprime(p = 3, oo, if(isprime(t), pit++); res[t-1] = floor(t * frac(p/pit)); t++; if(t-1 > n, return(res)))} \\ David A. Corneth, Aug 22 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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