A145583
a(n) = number of numbers removed in the n-th step of Eratosthenes's sieve for 10^2.
Original entry on oeis.org
Artur Jasinski with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008
Cf.
A006880,
A122121,
A145532,
A145533,
A145534,
A145535,
A145536,
A145537,
A145538,
A145539,
A145540,
A145583,
A145584,
A145585,
A145586,
A145587,
A145588,
A145589,
A145590,
A145591,
A145592.
-
f3[k_Integer?Positive, i_Integer?Positive] := Module[{f, m, r, p}, p = Transpose[{r = Range[2, i], Prime[r]}];f[x_] := Catch[Fold[If[Mod[x, #2[[2]]] == 0, Throw[m[ #2[[1]]] = m[ #2[[1]]] + 1], #1] &, If[Mod[x, 2] == 0, Throw[m[1] = m[1] + 1]], p]]; Table[m[n] = -1, {n, i}]; f /@ Range[k]; Table[m[n], {n, i}]];nn = 2; kk = PrimePi[Sqrt[10^nn]]; t3 = f3[10^nn, kk] (*Bob Hanlon (hanlonr(AT)cox.net) *)
A227155
Number of composites removed in each step of the Sieve of Eratosthenes for 10^7.
Original entry on oeis.org
4999999, 1666666, 666666, 380952, 207791, 159839, 112829, 95016, 74356, 56405, 50949, 41317, 36293, 33780, 30205, 26228, 23123, 21975, 19655, 18249, 17467, 15871, 14876, 13668, 12358, 11710, 11344, 10779, 10451, 9955, 8748, 8398, 7956, 7768, 7181, 7034, 6724
Offset: 1
For n = 2, prime(n) = 3, a(n) = 1666666: 3 divides 10^7 3333333 times.
6 is the common multiple of 2 and 3, thus 10^7 \ 6 multiples of 3 (1666666) have already been eliminated by a(1).
3333333 less 1666666 = 1666667, less 1 because 3 itself is not eliminated.
Thus a(2) = 3333333 - 1666666 - 1 = 1666666.
A227799
Number of composites removed in each step of the Sieve of Eratosthenes for 10^10.
Original entry on oeis.org
4999999999, 1666666666, 666666666, 380952380, 207792207, 159840159, 112828348, 95013343, 74358271, 56409724, 50950713, 41311372, 36273411, 33742734, 30153115, 26170720, 23065826, 21931483, 19640105, 18256894, 17506397, 15954848, 14993294, 13813524, 12531256
Offset: 1
a(1) = 10^10 \ 2 - 1.
a(2) = 10^10 \ 3 - 10^10 \ (2*3) - 1.
a(3) = 10^10 \ 5 - 10^10 \ (2*5) - 10^10 \ (3*5) + 10^10 \ (2*3*5) - 1.
a(4) = 10^10 \ 7 - 10^10 \ (2*7) - 10^10 \ (3*7) - 10^10 \ (5*7) + 10^10 \ (2*3*7) + 10^10 \ (2*5*7) + 10^10 \ (3*5*7) - 10^10 \ (2*3*5*7) - 1.
Cf.
A133228,
A145538,
A145539,
A145540,
A145583,
A227155,
A227797,
A227798,
A145532,
A145533,
A145534,
A145535,
A145536,
A145537.
A145584
a(n) = number of numbers removed in step n of Eratosthenes's sieve for 2^6.
Original entry on oeis.org
Artur Jasinski with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008
-
f3[k_Integer?Positive, i_Integer?Positive] := Module[{f, m, r, p}, p = Transpose[{r = Range[2, i], Prime[r]}];f[x_] := Catch[Fold[If[Mod[x, #2[[2]]] == 0, Throw[m[ #2[[1]]] = m[ #2[[1]]] + 1], #1] &, If[Mod[x, 2] == 0, Throw[m[1] = m[1] + 1]], p]]; Table[m[n] = -1, {n, i}]; f /@ Range[k]; Table[m[n], {n, i}]];nn = 6; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)
Showing 1-4 of 4 results.
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