|
|
A189153
|
|
The number of primes in A013918 less than 10^n.
|
|
1
|
|
|
2, 4, 6, 8, 22, 51, 118, 313, 796, 2022, 5460, 14756, 41508, 116504, 331022, 944930, 2716758, 7851206
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
It seems that sequence A013918 is infinite, but this has never been proved.
|
|
LINKS
|
|
|
FORMULA
|
Let x=10^n, then a(n) has the asymptotic expression a(n)~0.475*li( sqrt(4x/log(4x)) )
|
|
MATHEMATICA
|
p = Select[Accumulate[Prime[Range[100000]]], PrimeQ]; Table[Length[Select[p, # < 10^n &]], {n, Floor[Log[10., p[[-1]]]]}] (* T. D. Noe, Apr 19 2011 *)
|
|
PROG
|
(PARI)
PrimesInSumOfPrimes(n)=
{
local(p, s, w);
p=s=w=0;
while( s<=10^n,
if( isprime(s), w++ );
p = nextprime(p+1);
s = s + p;
);
return(w);
}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|