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 1-9 of 9 results.

A103591 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/2.

Original entry on oeis.org

1, 3, 10, 59, 1413, 361139, 4833601540, 43922730588128390
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Crossrefs

Programs

  • Mathematica
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/2, m++];
    m, {n, 1, 5}] (* Robert Price, Mar 27 2019 *)
  • PARI
    a(n) = my(s = 0, k = 1); while ((s += 1/prime(k)) < n/2, k++); k \\ Michel Marcus, Aug 22 2013

Formula

a(2n) = A046024(n). - Michel Marcus, Aug 22 2013

Extensions

a(7) from Robert Price, Dec 10 2013
a(8) derived from A046024 by Robert Price, Dec 10 2013

A103592 a(n) is the smallest prime p such that Sum_{primes q <= p} 1/q >= n/2.

Original entry on oeis.org

2, 5, 29, 277, 11789, 5195977, 118185163069, 1801241230056600523
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Crossrefs

Programs

  • Mathematica
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/2, m++];
    Prime[m], {n, 1, 8}] (* Robert Price, Mar 27 2019 *)

Extensions

a(7)-a(8) from Martin Raab, Aug 24 2008
a(7) corrected by Martin Raab, Mar 31 2009

A103599 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/6.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 6, 10, 16, 29, 59, 140, 400, 1413, 6467, 40261, 361139, 4990906, 114916199, 4833601540
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Comments

a(22) > 5*10^10. - Robert Price, Dec 10 2013

Crossrefs

Programs

  • Mathematica
    For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/6, Print[k]; Break[]]]] (* Robert Price, Dec 09 2013 *)
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/6, m++];
    m, {n, 1, 17}] (* Robert Price, Mar 27 2019 *)

Extensions

a(2)-a(4) and a(19)-a(21) added by Robert Price, Dec 10 2013

A103593 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/3.

Original entry on oeis.org

1, 2, 3, 6, 16, 59, 400, 6467, 361139, 114916199
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Comments

a(n) <= e^(e^(n/3)), therefore a(10) < 1492725701441. - Stefan Steinerberger, Mar 18 2006
a(11) > 5*10^10. - Robert Price, Dec 10 2013

Crossrefs

Programs

  • Mathematica
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/3, m++];
    m, {n, 1, 10}] (* Robert Price, Mar 27 2019 *)

Extensions

a(10) from Robert Price, Dec 10 2013

A103594 Smallest prime p such that Sum_{primes q <= p} 1/q >= n/3.

Original entry on oeis.org

2, 3, 5, 13, 53, 277, 2741, 64663, 5195977, 2358926351, 12041724518809, 1801241230056600523
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Crossrefs

Programs

  • Mathematica
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/3, m++];
    Prime[m], {n, 1, 10}] (* Robert Price, Mar 27 2019 *)

Extensions

a(10) from Robert Price, Dec 10 2013
a(11) and a(12) copied from A103600(22) and A016088(4), respectively, by Jon E. Schoenfield, Feb 01 2020

A103595 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/4.

Original entry on oeis.org

1, 1, 2, 3, 5, 10, 21, 59, 231, 1413, 15474, 361139, 22347214, 4833601540
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Comments

a(15) > 5*10^10. - Robert Price, Dec 10 2013

Crossrefs

Programs

  • Mathematica
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/4, m++];
    m, {n, 1, 14}] (* Robert Price, Mar 27 2019 *)

Extensions

a(1) and a(13)-a(14) from Robert Price, Dec 10 2013

A103596 Smallest prime p such that Sum_{primes q <= p} 1/q >= n/4.

Original entry on oeis.org

2, 2, 3, 5, 11, 29, 73, 277, 1453, 11789, 169751, 5195977, 420055319, 118185163069
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Comments

a(14) > pi(5*10^5). - Robert Price, Dec 10 2013

Crossrefs

Programs

  • Mathematica
    For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/4, Print[Prime[k]]; Break[]]]]
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/4, m++];
    Prime[m], {n, 1, 14}] (* Robert Price, Mar 27 2019 *)

Extensions

a(1) added by Robert Price, Dec 10 2013
a(13)-a(14) from Robert Price, Dec 10 2013

A103597 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/5.

Original entry on oeis.org

1, 1, 2, 2, 3, 5, 7, 13, 25, 59, 170, 644, 3402, 27178, 361139, 8947437, 474314304
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Comments

a(18) > 5*10^10. - Robert Price, Dec 10 2013

Crossrefs

Programs

  • Mathematica
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/5, m++];
    m, {n, 1, 17}] (* Robert Price, Mar 27 2019 *)

Extensions

a(2)-a(3) and a(16)-a(17) from Robert Price, Dec 10 2013

A103598 Smallest prime p such that Sum_{primes q <= p} 1/q >= n/5.

Original entry on oeis.org

2, 2, 3, 3, 5, 11, 17, 41, 97, 277, 1013, 4789, 31627, 314723, 5195977, 159490147, 10443979657
Offset: 1

Views

Author

James R. Buddenhagen, Mar 28 2005

Keywords

Comments

a(18) > pi(5*10^10). - Robert Price, Dec 10 2013

Crossrefs

Programs

  • Mathematica
    For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/5, Print[Prime[k]]; Break[]]]]
    Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/5, m++];
    Prime[m], {n, 1, 17}] (* Robert Price, Mar 27 2019 *)

Extensions

a(1)-a(2) and a(16)-a(17) from Robert Price, Dec 10 2013
Showing 1-9 of 9 results.