|
Search: id:A086680
|
|
|
| A086680 |
|
Number of primes < 4^n. |
|
+0
1
|
|
| 0, 2, 6, 18, 54, 172, 564, 1900, 6542, 23000, 82025, 295947, 1077871, 3957809, 14630843, 54400028, 203280221, 762939111, 2874398515, 10866266172, 41203088796, 156661034233, 597116381732, 2280998753949, 8731188863470
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
These numbers approximate the sum of primes < 2^n. The sum of primes < 2^20 =
A130739(20) = 41162256126. The number of primes < 2^40 = 41203088796. The
error is -0.000991993. From A007053, we have number of
primes < 2^74 =375744164937699609596 and sum of
primes < 2^37 =375743480734175191581 for an error of -0.0000018209325.
Justification sumprimes(n) ~ Pi(n^2) can br found in the link.
|
|
LINKS
|
Cino Hilliard, Sum of primes less than n [Cino Hilliard, Feb 13 2009]
|
|
EXAMPLE
|
for n=2, 2,3,5,7,11,13 are the 6 primes < 2^4.
|
|
CROSSREFS
|
Cf. A007053, A130739.
Sequence in context: A134635 A114464 A062415 this_sequence A148455 A094590 A004529
Adjacent sequences: A086677 A086678 A086679 this_sequence A086681 A086682 A086683
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2003
|
|
EXTENSIONS
|
Extended by Cino Hilliard (hillcino368(AT)hotmail.com), Feb 13 2009
|
|
|
Search completed in 0.002 seconds
|
