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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
Sequence in context: A277937 A334913 A112020 * A089616 A089615 A301593
KEYWORD
easy,nonn
AUTHOR
T. D. Noe, Apr 09 2002
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)