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A094019 An approximation to Prime(n) and pi(n). 0
2, 5, 7, 10, 14, 17, 21, 24, 28, 32, 36, 40, 44, 48, 53, 57, 62, 66, 71, 76, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 146, 151, 156, 162, 167, 172, 178, 183, 189, 194, 200, 206, 211, 217, 222, 228, 234, 239, 245, 251, 257, 262, 268, 274, 280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..58.

FORMULA

Let a(1)=2, S(1)=log(2), n=1; (*) n=n+1 a(n)=S(n-1)+(Pi)*i^(Pi/6) ( Pi=3.14159....), S(i)=S(i-1)+log(a(i)), a(i)=int(a(i)), goto (*).

EXAMPLE

a(i)=p(i) for i= 1,81,101,109,142,169,286,334,446,479,624,846,959,1019,1034....

pi(10) = 4 whereas sequence gives 3

pi(100) = 25 whereas sequence gives 24

pi(1000) = 168 whereas sequence gives 167

pi(10000) = 1229 whereas sequence gives 1226

pi(100000) = 9592 whereas sequence gives 9586

pi(1000000) = 78498 whereas sequence gives 78524

pi(10000000) = 664579 whereas sequence gives 664668

pi(100000000) = 5761455 whereas sequence gives 5761527

pi(1000000000) = 50847534 whereas sequence gives 50847381

pi(10000000000) = 455052511 whereas sequence gives 455050443

CROSSREFS

Sequence in context: A287403 A287399 A276213 * A161580 A024177 A276465

Adjacent sequences:  A094016 A094017 A094018 * A094020 A094021 A094022

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jun 02 2004

STATUS

approved

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Last modified November 22 01:14 EST 2019. Contains 329383 sequences. (Running on oeis4.)