A083269 a(n) = pi(A052180(n)) = A000720(A052180(n)); subscript of last prime used in Eratosthenes sieve by which all composites between n-th and (n+1)th primes were excluded.

0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 4, 3, 1, 3, 2, 1, 4, 2, 3, 4, 2, 1, 2, 1, 2, 5, 2, 4, 1, 5, 1, 3, 4, 2, 6, 3, 1, 5, 1, 2, 1, 5, 6, 2, 1, 2, 3, 1, 6, 5, 4, 3, 1, 3, 2, 1, 7, 6, 2, 1, 2, 7, 3, 5, 1, 2, 3, 8, 4, 6, 2, 3, 7, 2, 6, 4, 1, 4, 1, 8, 2, 3, 5, 2, 1, 2, 5, 6, 2, 7, 2, 3, 5, 1, 9, 3, 8, 6, 3, 1, 3

Offset

1,4

Links

Table of n, a(n) for n=1..105.

Example

Of composites between the 24th and 25th primes (89, 97), the least prime divisors are {2,7,2,3,2,5,2}.
The largest of these is 7. This means that pi(7)=4 steps in prime sieving are required to sweep out all composites between 89 and 97: {90,92,94,96}, (93}, {95}, and {91} were excluded in the 1st, 2nd, 3rd, and 4th steps, respectively.
So a(24)=4.

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] mi[x_] := Min[ba[x]] Table[PrimePi[Max[Table[mi[ba[w]], {w, Prime[j]+1, -1+Prime[j+1]}]]], {j, 1, 30}]

Crossrefs

Cf. A052180, A000720.

Sequence in context: A331366 A274225 A028334 * A097306 A102632 A094076

Adjacent sequences: A083266 A083267 A083268 * A083270 A083271 A083272

Keyword

nonn

Author

Labos Elemer, May 14 2003

Status

approved