|
|
A069160
|
|
Number of primes p such that n^2 < p < n^2 + pi(n), where pi(n) is the number of primes less than n.
|
|
1
|
|
|
0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 0, 1, 2, 2, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 2, 2, 3, 1, 2, 3, 1, 3, 2, 3, 1, 0, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 1, 2, 1, 1, 4, 2, 1, 2, 2, 3, 0, 2, 3, 3, 2, 2, 0, 2, 2, 2, 2, 3, 2, 3, 1, 3, 2, 1, 5, 2, 3, 2, 4, 2, 5, 3, 3, 4, 4, 1, 2, 3, 3, 3, 5, 3, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,10
|
|
COMMENTS
|
A more restrictive version of the conjecture that there is always a prime between n^2 and (n+1)^2.
|
|
LINKS
|
|
|
EXAMPLE
|
a(10)= 2 because pi(10) = 4 and there are 2 primes between 100 and 104.
|
|
MATHEMATICA
|
maxN=100; lst={}; For[i=1, i<maxN, i++, n=i^2; cnt=0; k=1; While[k<PrimePi[i], If[PrimeQ[n+k], cnt++ ]; k++ ]; AppendTo[lst, cnt]]; lst
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|