A145589 a(n) = number of numbers removed in each step of Eratosthenes's sieve for 2^11.

1023, 340, 136, 77, 41, 32, 24, 21, 16, 10, 8, 5, 3, 2

Offset: 1

Author

Artur Jasinski with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008

Keywords

• fini
• nonn

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).

Number of primes less than 2^11 is equal to 2^11 - (sum all of numbers in this sequence) - 1 = A007053(11).

Crossrefs

Cf. A006880, A122121, A145532-A145540, A145583-A145592.

Programs

Mathematica

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 = 11; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008 *)