A145592 a(n)=number of numbers removed in each step of Eratosthenes's sieve for 2^14.

8191, 2730, 1091, 623, 340, 260, 182, 154, 121, 94, 89, 74, 66, 62, 55, 48, 43, 39, 35, 31, 28, 25, 23, 19, 15, 12, 11, 9, 7, 5, 1

Offset: 1

Author

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

Keywords

• fini
• full
• nonn

Comments

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

Number of primes less than 2^14 is equal to 2^14 - (sum all of numbers in this sequence) - 1 = A007053(14).

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