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 1-8 of 8 results.

A136675 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^3.

Original entry on oeis.org

1, 7, 197, 1549, 195353, 194353, 66879079, 533875007, 14436577189, 14420574181, 19209787242911, 19197460851911, 42198121495296467, 6025866788581781, 6027847576222613, 48209723660000029, 236907853607882606477
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

a(n) is prime for n in A136683.
Lim_{n -> infinity} a(n)/A334582(n) = A197070. - Petros Hadjicostas, May 07 2020

Examples

			The first few fractions are 1, 7/8, 197/216, 1549/1728, 195353/216000, 194353/216000, 66879079/74088000, 533875007/592704000, ... = a(n)/A334582(n). - _Petros Hadjicostas_, May 06 2020

Links

Crossrefs

Cf. A001008, A007406, A007408, A007410, A058313, A099828, A103345, A119682, A120296, A136676, A136677, A136681, A136682, A136683, A136684, A136685, A136686, A197070, A334582 (denominators).

Programs

  • Maple
    map(numer,ListTools:-PartialSums([seq((-1)^(k+1)/k^3, k=1..100)])); # Robert Israel, Nov 09 2023
  • Mathematica
    (* Program #1 *) Table[Numerator[Sum[(-1)^(k+1)/k^3, {k,1,n}]], {n,1,50}]
(* Program #2 *) Numerator[Accumulate[Table[(-1)^(k+1) 1/k^3, {k,50}]]] (* Harvey P. Dale, Feb 12 2013 *)
  • PARI
    a(n) = numerator(sum(k=1, n, (-1)^(k+1)/k^3)); \\ Michel Marcus, May 07 2020

A136677 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^6.

Original entry on oeis.org

1, 63, 45991, 2942695, 45982595359, 5109066151, 601081707598999, 38469080386820311, 252396118308232060471, 252395862211967012407, 447134922152359540530757327, 447134770212444455649757327, 2158234586764514215343657417779543, 308319185132349039219686748825649
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

p divides a(p-1) for prime p > 2. a(n) is prime for n = {19, 47, 164, ...} = A136686.
Lim_{n -> infinity} a(n)/A334605(n) = A275703 = (31/32)*A013664. - Petros Hadjicostas, May 07 2020

Examples

			The first few fractions are 1, 63/64, 45991/46656, 2942695/2985984, 45982595359/46656000000, 5109066151/5184000000, ... = a(n)/A334605(n). - _Petros Hadjicostas_, May 07 2020

Links

Crossrefs

Cf. A013664, A058313, A119682, A120296, A136675, A136676.
Cf. A001008, A007406, A007408, A007410, A099828, A103345, A275703.
Cf. A136681, A136682, A136683, A136684, A136685, A136686, A334605 (denominators).

Programs

  • Mathematica
    Table[ Numerator[ Sum[ (-1)^(k+1)/k^6, {k,1,n} ] ], {n,1,30} ]
Accumulate[Table[(-1)^(k+1)/k^6,{k,20}]]//Numerator (* Harvey P. Dale, Aug 21 2023 *)

A136676 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^5.

Original entry on oeis.org

1, 31, 7565, 241837, 755989457, 755889457, 12705011703799, 406547611705943, 98792790681344149, 98791774426324117, 15910615688635928566967, 15910549913780913466967, 5907492176026179821253778331
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

a(n) is prime for n in A136685.
Lim_{n -> infinity} a(n)/A334604(n) = A267316 = (15/16)*A013663. - Petros Hadjicostas, May 07 2020

Examples

			The first few fractions are 1, 31/32, 7565/7776, 241837/248832, 755989457/777600000, 755889457/777600000, ... = a(n)/A334604(n). - _Petros Hadjicostas_, May 07 2020

Links

Crossrefs

Cf. A001008, A007406, A007408, A007410, A013663, A058313, A099828, A103345, A119682, A120296, A136675, A136677, A136681, A136682, A136683, A136684, A136685, A136686, A267316, A334604 (denominators).

Programs

  • Mathematica
    Table[ Numerator[ Sum[ (-1)^(k+1)/k^5, {k,1,n} ] ], {n,1,30} ]
  • PARI
    a(n) = numerator(sum(k=1, n, (-1)^(k+1)/k^5)); \\ Michel Marcus, May 07 2020

A136681 Numbers k such that A058313(k) is prime.

Original entry on oeis.org

3, 4, 5, 6, 9, 10, 13, 16, 17, 18, 37, 43, 58, 121, 124, 126, 137, 203, 247, 283, 285, 286, 289, 317, 424, 508, 751, 790, 937, 958, 1066, 1097, 1151, 1166, 1194, 1199, 1235, 1414, 1418, 1460, 1498, 1573, 2090, 2122, 2691, 2718, 3030, 3426, 3600, 3653, 3737
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

A058313(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j.

Links

Crossrefs

Cf. A058313, A119682, A120296, A136675, A136676, A136677.
Cf. A001008, A007406, A007408, A007410, A099828, A103345.
Cf. A136682, A136683, A136684, A136685, A136686.

Programs

  • Mathematica
    Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,317} ]
  • PARI
    isok(n) = isprime(numerator(sum(k=1, n, (-1)^(k+1)/k))); \\ Michel Marcus, Mar 14 2019

Extensions

a(25)-a(30) from James R. Buddenhagen, Sep 22 2015
a(31)-a(51) from Amiram Eldar, Mar 14 2019

A136682 Numbers k such that A119682(k) is prime.

Original entry on oeis.org

2, 3, 5, 8, 23, 41, 47, 48, 49, 95, 125, 203, 209, 284, 323, 395, 504, 553, 655, 781, 954, 1022, 1474, 1797, 1869, 1923, 1934, 1968, 2043, 2678, 3413, 3439, 4032, 4142, 4540, 4895, 5018, 5110, 5194, 5357, 6591, 11504, 11949, 14084, 20365
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

A119682(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j^2.

Links

Crossrefs

Cf. A058313, A119682, A120296, A136675, A136676, A136677.
Cf. A001008, A007406, A007408, A007410, A099828, A103345.
Cf. A136681, A136683, A136684, A136685, A136686.

Programs

  • Mathematica
    Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k^2, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,125} ]

Extensions

a(12)-a(17) from Alexander Adamchuk, Apr 28 2008
a(18)-a(31) from Amiram Eldar, Mar 14 2019
a(32)-a(45) from Robert Price, Apr 14 2019

A136683 Numbers k such that A136675(k) is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 9, 20, 21, 29, 119, 132, 151, 351, 434, 457, 462, 572, 611, 930, 1107, 1157, 1452, 1515, 2838, 3997, 5346, 6463, 6725, 7664, 10234, 14168, 14299
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

A136675(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j^3.

Links

Crossrefs

Cf. A058313, A119682, A120296, A136675, A136676, A136677.
Cf. A001008, A007406, A007408, A007410, A099828, A103345.
Cf. A136681, A136682, A136684, A136685, A136686.

Programs

  • Mathematica
    Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k^3, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,151} ]
Flatten[Position[Numerator[Accumulate[Table[(-1)^(k+1) 1/k^3,{k,3000}]]],?PrimeQ] ] (* _Harvey P. Dale, Feb 12 2013 *)
  • PARI
    isok(n) = ispseudoprime(numerator(sum(k=1, n, (-1)^(k+1) / k^3))); \\ Daniel Suteu, Mar 15 2019

Extensions

More terms from Harvey P. Dale, Feb 12 2013
a(25)-a(28) from Amiram Eldar, Mar 15 2019
a(29)-a(32) from Robert Price, Apr 22 2019

A136684 Numbers k such that A120296(k) is prime.

Original entry on oeis.org

3, 5, 8, 11, 20, 38, 61, 65, 71, 80, 83, 93, 233, 704, 1649, 2909, 3417, 3634, 9371
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

A120296(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j^4.

Links

Crossrefs

Cf. A058313, A119682, A136675, A120296, A136676, A136677.
Cf. A001008, A007406, A007408, A007410, A099828, A103345.
Cf. A136681, A136682, A136683, A136685, A136686.

Programs

  • Mathematica
    Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k^4, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,100} ]
Select[Range[1000],PrimeQ[Numerator[Sum[(-1)^(k+1) 1/k^4,{k,#}]]]&] (* Harvey P. Dale, Aug 28 2012 *)

Extensions

More terms from Harvey P. Dale, Aug 28 2012
a(15)-a(19) from Robert Price, Apr 23 2019

A136685 Numbers k such that A136676(k) is prime.

Original entry on oeis.org

2, 19, 51, 78, 84, 130, 294, 910, 2223, 2642, 3261, 4312, 4973, 7846, 9439
Offset: 1

Views

Author

Alexander Adamchuk, Jan 16 2008

Keywords

Comments

A136676(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j^5.

Links

Crossrefs

Cf. A058313, A119682, A136675, A120296, A136676, A136677.
Cf. A001008, A007406, A007408, A007410, A099828, A103345.
Cf. A136681, A136682, A136683, A136684, A136686.

Programs

  • Mathematica
    Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k^5, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,130} ]

Extensions

a(7)-a(8) from Amiram Eldar, Mar 14 2019
a(9)-a(15) from Robert Price, Apr 16 2019
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.