A094019 An approximation to Prime(n) and pi(n).

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

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 A360456

Adjacent sequences: A094016 A094017 A094018 * A094020 A094021 A094022

Keyword

nonn

Author

Pierre CAMI, Jun 02 2004

Status

approved