

A083269


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


3



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
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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*w1], {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



