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.

Previous Showing 11-19 of 19 results.

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) *)

A379566 Number of n-digit numbers that have exactly 3 divisors.

Original entry on oeis.org

2, 2, 7, 14, 40, 103, 278, 783, 2172, 6191, 17701, 51205, 149149, 436932, 1287378, 3809498, 11321211, 33764868, 101029398, 303175579, 912147300, 2750855002, 8313825647, 25176031558, 76375623757, 232082001064, 706304629714, 2152571584249, 6568923555719
Offset: 1

Views

Author

Seiichi Manyama, Dec 26 2024

Keywords

Crossrefs

Column k=3 of A284398.
Cf. A001248, A006880, A122121.

Formula

a(n) = A122121(n) - A122121(n-1).

Extensions

a(18)-a(29) from Seiichi Manyama using A122121 data, Dec 26 2024
Previous Showing 11-19 of 19 results.

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