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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

T. D. Noe, Table of n, a(n) for n=1..10000

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

Cf. A000720, A014085.

Sequence in context: A205593 A277937 A112020 * A089616 A089615 A301593

Adjacent sequences:  A069157 A069158 A069159 * A069161 A069162 A069163

KEYWORD

easy,nonn

AUTHOR

T. D. Noe, Apr 09 2002

STATUS

approved

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Last modified April 3 21:54 EDT 2020. Contains 333207 sequences. (Running on oeis4.)