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A217254 a(n) = round(primepi(n) * prime(n)/n). 1
0, 2, 3, 4, 7, 7, 10, 10, 10, 12, 14, 15, 19, 18, 19, 20, 24, 24, 28, 28, 28, 29, 32, 33, 35, 35, 34, 34, 38, 38, 45, 45, 46, 45, 47, 46, 51, 51, 51, 52, 57, 56, 62, 61, 61, 61, 67, 70, 69, 69, 69, 69, 73, 74, 75, 75, 76, 75, 80, 80, 84, 85, 88, 87, 87, 86, 94 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Apparently in the beginning of this sequence, there are very few occasions, particularly at indexes 14, 27, 34, 36, 42, 44, 49, 58, 64, 66 where the next sequence's term is smaller than the previous one. It may be interesting to notice that all above listed indexes are composite numbers. On another hand the growth of this sequence is very slow, with seems to be the pattern of occasional terms value repetition occurrences (one could observe that those repetitive terms appear in the beginning of this sequence in groups of two, three and/or four) - thus the growth of this sequence in its beginning is much slower than the growth of the natural progression of primes themselves.

For n < 10^7, a(n-1) > a(n) happens only for n composite. For n < 10^8, a(n-1) - a(n) <= 2. On the contrary, a(n) - a(n-1) seems to grow slowly and up to 10^5, 10^6, 10^7 and 10^8 is equal to 21, 26, 30, and 34, respectively. - Giovanni Resta, Mar 21 2013

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

FORMULA

a(n) ~ n. More specifically, a(n) = n + n log log n/log n + 2n log log n/log^2 n + O(n/log^2 n); the O-constant is between -1/2 and -3/2 for large n. - Charles R Greathouse IV, Mar 19 2013

MATHEMATICA

Table[Floor[PrimePi[n]*Prime[n]/n + 1/2], {n, 100}] (* T. D. Noe, Mar 20 2013 *)

PROG

(PARI) a(n)=prime(n)*primepi(n)\/n \\ Charles R Greathouse IV, Mar 19 2013

CROSSREFS

Cf. A128930.

Sequence in context: A265368 A239972 A162425 * A223488 A175686 A305563

Adjacent sequences:  A217251 A217252 A217253 * A217255 A217256 A217257

KEYWORD

nonn,less,easy

AUTHOR

Alexander R. Povolotsky, Mar 16 2013

STATUS

approved

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Last modified April 3 14:34 EDT 2020. Contains 333197 sequences. (Running on oeis4.)