A189024 Number of primes in the range (n - sqrt(n), n].

0, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 0, 0, 1

Offset

1,3

Comments

Note that the lower bound, n-sqrt(n), is excluded from the count and the upper range, n, is included. The last zero term appears to be a(126). See A189026 for special primes associated with this sequence. This sequence is related to Oppermann's conjecture that for any k > 1 there is a prime between k^2 - k and k^2.

Links

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

Wikipedia, Oppermann's conjecture

Mathematica

cnt = 0; lastLower = 0; Table[lower = Floor[n - Sqrt[n]]; If[lastLower < lower && PrimeQ[lower], cnt--]; lastLower = lower; If[PrimeQ[n], cnt++]; cnt, {n, 100}]
Table[PrimePi[n]-PrimePi[n-Sqrt[n]], {n, 130}] (* Harvey P. Dale, Mar 26 2023 *)

Crossrefs

Cf. A188817, A189025, A189027.

Sequence in context: A063053 A063050 A330098 * A304720 A057557 A353364

Adjacent sequences: A189021 A189022 A189023 * A189025 A189026 A189027

Keyword

nonn

Author

T. D. Noe, Apr 15 2011

Status

approved