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 14 results. Next

A213365 Numbers k such that 3*k is a partition number.

Original entry on oeis.org

1, 5, 10, 14, 45, 77, 99, 209, 264, 334, 525, 812, 1868, 2783, 3381, 4961, 10395, 12446, 14861, 21087, 35186, 49091, 79981, 93863, 109977, 204718, 373835, 501833, 1029245, 1362656, 1565735, 2706088, 5265492, 14702703, 44410310, 80421793, 101600455, 128092112, 143716463, 226634401, 354714817, 947313500, 1054375784
Offset: 1

Views

Author

Omar E. Pol, Jan 08 2013

Keywords

Comments

Is this sequence infinite? Klarreich writes: no one has proved whether there are infinitely many partition numbers divisible by 3 (see Jonathan Vos Post's comment in A000041 and A087183). - Omar E. Pol, Jan 14 2014

Links

Crossrefs

Cf. A000041, A087183, A213179, A216258, A217725, A217726, A222175, A222178, A222179, A225317, A225323.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 3] == 0 &]/3 (* Omar E. Pol, May 07 2013 *)

Formula

a(n) = A087183(n)/3.

Extensions

a(35)-a(43) from R. J. Mathar, May 05 2013

A225324 Partition numbers of the form 4k.

Original entry on oeis.org

56, 176, 792, 2436, 5604, 451276, 715220, 831820, 1300156, 2323520, 4087968, 7089500, 8118264, 12132164, 15796476, 26543660, 92669720, 118114304, 150198136, 190569292, 384276336, 483502844, 541946240, 761002156, 851376628, 1188908248, 1327710076, 1844349560
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008586 and A000041.

Examples

			56 is in the sequence because 4*14 = 56 and 56 is a partition number: p(11) = A000041(11) = 56.

Links

Crossrefs

Cf. A000041, A008586, A052001, A072871, A087183, A127544, A216258, A225325, A225326, A225327, A225358, A225360, A225361, A237278.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 4] == 0 &] (* T. D. Noe, May 05 2013 *)
  • PARI
    for(n=9, 1e3, t=numbpart(n); if(t%4, , print1(t", "))) \\ Charles R Greathouse IV, May 08 2013

Formula

a(n) = 4*A216258(n). - Omar E. Pol, May 08 2013
a(n) = A000041(A237278(n)). - Amiram Eldar, May 22 2025

Extensions

a(6)-a(28) from T. D. Noe, May 05 2013

A127544 Partition numbers (A000041) which are multiples of 10 (A008592).

Original entry on oeis.org

30, 490, 3010, 12310, 715220, 831820, 1741630, 2323520, 7089500, 13848650, 26543660, 92669720, 133230930, 271248950, 541946240, 1844349560, 2841940500, 4351078600, 4835271870, 5371315400, 10015581680, 18440293320, 37027355200
Offset: 1

Views

Author

Zak Seidov, Apr 01 2007

Keywords

Comments

Intersection of A000041 and A008592.
Partition numbers of the form 10k. - Omar E. Pol, May 08 2013

Crossrefs

Cf. A000041, A052001, A008592, A087183.

Programs

  • Mathematica
    Select[Table[PartitionsP[n],{n,0,200}],Mod[ #,10]==0&]

Formula

a(n) = 10*A225317(n). - Omar E. Pol, May 08 2013

Extensions

Corrected by Omar E. Pol, May 05 2013

A225325 Partition numbers of the form 5k.

Original entry on oeis.org

5, 15, 30, 135, 385, 490, 1255, 1575, 3010, 4565, 12310, 26015, 31185, 75175, 173525, 386155, 715220, 831820, 1121505, 1741630, 2323520, 3087735, 3554345, 4697205, 7089500, 13848650, 20506255, 26543660, 49995925, 92669720, 133230930, 169229875
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008587 and A000041.

Examples

			15 is in the sequence because 5*3 = 15 and 15 is a partition number: p(7) = A000041(7) = 15.

Links

Crossrefs

Cf. A000041, A008587, A052001, A072871, A087183, A225324, A225326, A225327, A225358, A225360, A127544, A225361

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 5] == 0 &] (* T. D. Noe, May 05 2013 *)
  • PARI
    for(n=9, 1e3, t=numbpart(n); if(t%5, , print1(t", "))) \\ Charles R Greathouse IV, May 08 2013

Formula

a(n) = 5*A217725(n). - Omar E. Pol, May 08 2013

A225326 Partition numbers of the form 6k.

Original entry on oeis.org

30, 42, 792, 1002, 2436, 5604, 37338, 105558, 614154, 4087968, 8118264, 15796476, 133230930, 384276336, 2841940500, 3163127352, 4835271870, 7346629512, 18440293320, 30388671978, 45060624582, 107438159466, 142798995930, 684957390936, 1820701100652
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008588 and A000041.

Examples

			30 is in the sequence because 6*5 = 30 and 30 is a partition number: p(9) = A000041(9) = 30.

Links

Crossrefs

Cf. A000041, A008588, A052001, A072871, A087183, A225324, A225325, A225327, A225358, A225360, A127544, A225361

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 6] == 0 &] (* T. D. Noe, May 05 2013 *)
  • PARI
    for(n=9,1e3,t=numbpart(n);if(t%6,,print1(t", "))) \\ Charles R Greathouse IV, May 08 2013

Formula

a(n) = 6*A217726(n). - Omar E. Pol, May 08 2013

Extensions

a(8)-a(25) from T. D. Noe, May 05 2013

A225327 Partition numbers of the form 7k.

Original entry on oeis.org

7, 42, 56, 77, 231, 385, 490, 1575, 2436, 3010, 10143, 21637, 31185, 37338, 44583, 124754, 147273, 281589, 329931, 386155, 451276, 1121505, 3087735, 8118264, 9289091, 20506255, 23338469, 49995925, 118114304, 133230930, 271248950, 607163746
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008589 and A000041.

Examples

			42 is in the sequence because 7*6 = 42 and 42 is a partition number: p(10) = A000041(10) = 42.

Links

Crossrefs

Cf. A000041, A008589, A052001, A072871, A087183, A225324, A225325, A225326, A225358, A225360, A127544, A225361.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 7] == 0 &]

Formula

a(n) = 7*A222175(n).

A225358 Partition numbers of the form 8k.

Original entry on oeis.org

56, 176, 792, 2323520, 4087968, 8118264, 92669720, 118114304, 150198136, 384276336, 541946240, 1188908248, 1844349560, 2291320912, 3163127352, 4351078600, 5371315400, 5964539504, 7346629512, 10015581680, 11097645016, 16670689208, 18440293320
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008590 and A000041.

Examples

			56 is in the sequence because 8*7 = 56 and 56 is a partition number: p(11) = A000041(11) = 56.

Links

Crossrefs

Cf. A000041, A008590, A052001, A072871, A087183, A225324, A225325, A225326, A225327, A225360, A127544, A225361.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 8] == 0 &]

Formula

a(n) = 8*A222178(n).

A225360 Partition numbers of the form 9k.

Original entry on oeis.org

135, 297, 792, 1575, 10143, 31185, 63261, 329931, 15796476, 44108109, 4835271870, 7346629512, 12292341831, 18440293320, 107438159466, 129913904637, 156919475295, 250438925115, 1527273599625, 3345365983698, 3646072432125, 7206841706490
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008591 and A000041.

Examples

			135 is in the sequence because 9*15 = 135 and 135 is a partition number: p(14) = A000041(14) = 135.

Links

Crossrefs

Cf. A000041, A008591, A052001, A072871, A087183, A225324, A225325, A225326, A225327, A225358, A127544, A225361.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 9] == 0 &]

Formula

a(n) = 9*A222179(n).

A225361 Partition numbers of the form 11k.

Original entry on oeis.org

11, 22, 77, 176, 231, 297, 385, 627, 792, 1958, 3718, 4565, 6842, 8349, 14883, 21637, 26015, 31185, 44583, 53174, 63261, 173525, 204226, 239943, 281589, 386155, 526823, 715220, 831820, 1121505, 1300156, 1741630, 5392783, 7089500, 8118264, 12132164, 18004327
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008593 and A000041.

Examples

			22 is in the sequence because 11*2 = 22 and 22 is a partition number: p(8) = A000041(8) = 22.

Crossrefs

Cf. A000041, A008593, A052001, A072871, A087183, A225324, A225325, A225326, A225327, A225358, A225360, A127544.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 11] == 0 &]

Formula

a(n) = 11*A225323(n).

A083214 Numbers k for which 3 | p(k), where p(k) = A000041(k) is the k-th partition number.

Original entry on oeis.org

3, 7, 9, 10, 14, 16, 17, 20, 21, 22, 24, 26, 30, 32, 33, 35, 39, 40, 41, 43, 46, 48, 51, 52, 53, 57, 61, 63, 68, 70, 71, 75, 80, 88, 97, 102, 104, 106, 107, 111, 115, 124, 125, 129, 133, 138, 142, 147, 151, 160, 162, 163, 164, 169, 173, 178, 180, 181, 189, 191, 193
Offset: 1

Views

Author

Jon Perry, Jun 01 2003

Keywords

Examples

			A000041(7)=15=0 mod 3.

Links

Crossrefs

Cf. A000041, A087183, A243935.

Programs

  • Mathematica
    Select[Range[250],Mod[PartitionsP[ # ],3]==0&] (* Zak Seidov, Apr 03 2007 *)
  • PARI
    { v=[1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,385,490,627,792,1002,1255,1575,1958,2436,3010,3718,4565,5604,6842,8349,10143,12310,14883,17977,21637,26015,31185,37338,44583,53174,63261,75175,89134]; for (i=2,length(v)-1,if (v[i]%3==0,print1(i-1","))) }
  • PARI
    for(n=1,300,if(polcoeff(1/eta(x)+O(x^(n+1)),n)%3==0,print1(n,","))) \\ Benoit Cloitre, Oct 06 2005
  • PARI
    is(n)=numbpart(n)%3==0 \\ Charles R Greathouse IV, Apr 08 2015

Formula

Conjecture : a(n) = 3n + o(n). - Benoit Cloitre, Oct 06 2005
A000041(a(n)) = A087183(n). - Zak Seidov, Apr 03 2007

Extensions

More terms from Benoit Cloitre, Oct 06 2005
Showing 1-10 of 14 results. Next

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