

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
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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(n1) > a(n) happens only for n composite. For n < 10^8, a(n1)  a(n) <= 2. On the contrary, a(n)  a(n1) 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 Oconstant 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



