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 A189025 Number of primes in the range (n - 2*sqrt(n), n]. 7
 0, 1, 2, 2, 3, 3, 4, 3, 2, 2, 3, 2, 3, 3, 2, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 4, 3, 4, 4, 3, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 4, 4, 5, 4, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 5, 4, 4, 4, 5, 5, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 3, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Note that the lower bound, n-2*sqrt(n), is excluded from the count and the upper range, n, is included. The only zero term appears to be a(1). See A189027 for special primes associated with this sequence. This sequence is related to Legendre's conjecture that there is a prime between consecutive squares. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Wikipedia, Legendre's conjecture MATHEMATICA cnt = 0; lastLower = -3; Table[lower = Floor[n - 2*Sqrt[n]]; If[lastLower < lower && PrimeQ[lower], cnt--]; lastLower = lower; If[PrimeQ[n], cnt++]; cnt, {n, 100}] PROG (PARI) a(n)=if(n

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Last modified June 2 11:35 EDT 2020. Contains 334771 sequences. (Running on oeis4.)