cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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) *)

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

Views

Author

Eric F. O'Brien, Jul 31 2013

Keywords

Comments

a(n) = the number of composites <= 10^10 for which the n-th prime is the least prime factor.
pi(sqrt(10^10)) = the number of terms of this sequence.
The sum of a(n) for n = 1..3401 = A000720(10^10) + A065855(10^10).

Examples

			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.

Links

Crossrefs

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

31, 10, 3, 1
Offset: 1

Views

Author

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

Keywords

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
Number of primes less than 2^6 is equal to 2^6 - (sum all of numbers in this sequence) - 1 = A007053(6).

Crossrefs

Cf. A006880, A122121.
Cf. A145532, A145533, A145534, A145535, A145536, A145537, A145538, A145539, A145540.
Cf. A145583, A145584, A145585, A145586, A145587, A145588, A145589, A145590, A145591, 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 = 6; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)

A145585 a(n) = number of numbers removed in each step of Eratosthenes's sieve for 2^7.

Original entry on oeis.org

63, 20, 8, 4, 1
Offset: 1

Views

Author

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

Keywords

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
Number of primes less than 2^7 is equal to 2^7 - (sum all of numbers in this sequence) - 1 = A007053(7).

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 = 7; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)

A145586 a(n) = number of numbers removed in each step of Eratosthenes's sieve for 2^8.

Original entry on oeis.org

127, 42, 16, 8, 5, 3
Offset: 1

Views

Author

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

Keywords

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
Number of primes less than 2^8 is equal to 2^8 - (sum all of numbers in this sequence) - 1 = A007053(8).

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 = 8; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008 *)

A145587 a(n) = number of numbers removed in each step of Eratosthenes's sieve for 2^9.

Original entry on oeis.org

255, 84, 33, 19, 10, 7, 4, 2
Offset: 1

Views

Author

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

Keywords

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
Number of primes less than 2^9 is equal to 2^9 - (sum all of numbers in this sequence) - 1 = A007053(9).

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 = 9; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008 *)

A145588 a(n) = number of numbers removed in each step of Eratosthenes's sieve for 2^10.

Original entry on oeis.org

511, 170, 67, 38, 20, 16, 11, 9, 6, 2, 1
Offset: 1

Views

Author

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

Keywords

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
Number of primes less than 2^10 is equal to 2^10 - (sum all of numbers in this sequence) - 1 = A007053(10).

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 = 10; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008 *)

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

Original entry on oeis.org

1023, 340, 136, 77, 41, 32, 24, 21, 16, 10, 8, 5, 3, 2
Offset: 1

Views

Author

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

Keywords

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 *)

A145590 a(n)=number of numbers removed in each step of Eratosthenes's sieve for 2^12.

Original entry on oeis.org

2047, 682, 272, 155, 83, 65, 46, 40, 32, 25, 22, 18, 13, 11, 9, 6, 3, 2
Offset: 1

Views

Author

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

Keywords

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
Number of primes less than 2^12 is equal to 2^12 - (sum all of numbers in this sequence) - 1 = A007053(12).

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 = 12; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)

A145591 a(n)=number of numbers removed in each step of Eratosthenes's sieve for 2^13.

Original entry on oeis.org

4095, 1364, 545, 311, 170, 130, 91, 77, 63, 51, 46, 36, 34, 29, 26, 21, 17, 15, 12, 11, 9, 6, 3, 1
Offset: 1

Views

Author

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

Keywords

Comments

Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
Number of primes less than 2^13 is equal to 2^13 - (sum all of numbers in this sequence) - 1 = A007053(13).

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 = 13; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)
Showing 1-10 of 10 results.

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