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 31-37 of 37 results.

A295593 Numbers k such that Bernoulli number B_{k} has denominator 230010.

Original entry on oeis.org

80, 160, 320, 13360, 17840, 18160, 20560, 25360, 26720, 28240, 30640, 35680, 36320, 36560, 41120, 43280, 45520, 46960, 50720, 52880, 56480, 60080, 61280, 69040, 70960, 71360, 72560, 72640, 79280, 84080, 87760, 91040, 92240, 93040, 93680, 93920, 94480, 97040, 97360
Offset: 1

Views

Author

Paolo P. Lava, Nov 24 2017

Keywords

Comments

230010 = 2*3*5*11*17*41.
All terms are multiples of a(1) = 80.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 182293.

Examples

			Bernoulli B_{80} is
-4603784299479457646935574969019046849794257872751288919656867/230010, hence 80 is in the sequence.

Links

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

  • Maple
    with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,230010);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 11, 17, 41}:
select(filter, [seq(i, i=1..10^5)]);

A295594 Numbers k such that Bernoulli number B_{k} has denominator 272118.

Original entry on oeis.org

90, 14670, 24210, 35010, 40410, 41670, 44910, 46890, 55530, 57870, 60570, 60930, 82710, 83610, 87030, 89730, 98370, 101070, 104670, 106830, 109530, 111330, 113310, 114930, 117090, 117270, 117630, 123570, 128610, 138870, 150030, 152730, 160470, 175590, 178110, 179730
Offset: 1

Views

Author

Paolo P. Lava, Nov 24 2017

Keywords

Comments

272118 = 2*3*7*11*19*31.
All terms are multiples of a(1) = 90.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 230759.

Links

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

  • Maple
    with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 272118);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 7, 11, 19, 31}:
select(filter, [seq(i, i=1..10^5)]);

Formula

272118 = 2*3*7*11*19*31.
Bernoulli B_{90} is
1179057279021082799884123351249215083775254949669647116231545215727922535/ 272118 hence 90 is in the sequence.

A295596 Numbers k such that Bernoulli number B_{k} has denominator 3404310.

Original entry on oeis.org

84, 168, 16548, 26628, 29316, 38388, 43764, 47964, 53256, 61572, 69132, 71988, 72156, 73668, 87528, 96852, 103908, 109284, 121548, 123144, 124572, 137508, 139188, 142548, 144312, 144564, 146244, 147336, 156828, 163716, 167748, 172452, 174972, 185388, 188076, 190428
Offset: 1

Views

Author

Paolo P. Lava, Nov 24 2017

Keywords

Comments

3404310 = 2*3*5*7*13*29*43.
All terms are multiples of a(1) = 84.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 2346073.

Examples

			Bernoulli B_{84} is
-2024576195935290360231131160111731009989917391198090877281083932477/3404310 hence 84 is in the sequence.

Links

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

  • Maple
    with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 3404310);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 7, 13, 29, 43}:
select(filter, [seq(i, i=1..10^5)]);

A295597 Numbers k such that Bernoulli number B_{k} has denominator 4501770.

Original entry on oeis.org

96, 20256, 42144, 56352, 62112, 70368, 84576, 105312, 119904, 146208, 155616, 156192, 165408, 167136, 168864, 183648, 187296, 200352, 200544, 204576, 217824, 221664, 228192, 234336, 240288, 252768, 255072, 255264, 258144, 262176, 263904, 266592, 274272, 304224, 306336
Offset: 1

Views

Author

Paolo P. Lava, Nov 24 2017

Keywords

Comments

4501770 = 2*3*5*7*13*17*97.
All terms are multiples of a(1) = 96.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 3051091.

Examples

			Bernoulli B_{96} is
-211600449597266513097597728109824233673043954389060234150638733420050668349987 259/4501770 hence 96 is in the sequence.

Links

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

  • Maple
    with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 4501770);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 7, 13, 17, 97}:
select(filter, [seq(i, i=1..10^5)]);
  • Mathematica
    96*Flatten[Position[BernoulliB[Range[96,31*10^4,96]],?(Denominator[ #] == 4501770&)]] (* The program takes a long time to run *) (* _Harvey P. Dale, May 06 2018 *)

A295598 Numbers k such that Bernoulli number B_{k} has denominator 56786730.

Original entry on oeis.org

60, 13620, 21180, 23340, 26940, 31260, 40620, 45420, 49620, 52620, 58020, 59460, 69780, 73020, 74220, 78180, 79140, 83940, 89580, 97260, 97620, 100020, 104460, 111660, 116940, 117060, 119820, 123180, 125340, 127860, 137820, 140460, 142260, 142620, 157980, 162420
Offset: 1

Views

Author

Paolo P. Lava, Nov 24 2017

Keywords

Comments

56786730 = 2*3*5*7*11*13*31*61.
All terms are multiples of a(1) = 60.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 34488049.

Examples

			Bernoulli B_{60} is
-1215233140483755572040304994079820246041491/56786730, hence 60 is in the sequence.

Links

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

  • Maple
    with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 56786730);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 7, 11, 13, 31, 61}:
select(filter, [seq(i, i=1..10^5)]);

A295599 Numbers k such that Bernoulli number B_{k} has denominator 140100870.

Original entry on oeis.org

72, 12024, 22824, 25416, 31608, 39384, 52776, 61848, 78984, 90648, 93672, 93816, 107496, 117864, 123912, 124056, 125784, 143784, 147816, 150408, 156888, 161064, 161208, 163368, 165384, 166248, 170712, 178056, 180216, 188424, 191304, 193608, 197928, 199944, 204696
Offset: 1

Views

Author

Paolo P. Lava, Nov 24 2017

Keywords

Comments

140100870 = 2*3*5*7*13*19*37*73.
All terms are multiples of a(1) = 72.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 91560011.

Examples

			140100870 = 2*3*5*7*13*19*37*73.
Bernoulli B_{72} is
-5827954961669944110438277244641067365282488301844260429/140100870, hence 72 is in the sequence.

Links

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

  • Maple
    with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 140100870);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 7, 13, 19, 37, 73}:
select(filter, [seq(i, i=1..10^5)]);

A295770 Numbers k such that Bernoulli number B_{k} has denominator 4686.

Original entry on oeis.org

70, 350, 4970, 5110, 7070, 8890, 9590, 9730, 13790, 15610, 15890, 16030, 17990, 18410, 19810, 21770, 22190, 23170, 24290, 25550, 26530, 26810, 27230, 28070, 30310, 32270, 32690, 33530, 34930, 36470, 38990, 39830, 40390, 43190, 44450, 45010, 48650, 49070, 49630, 51730
Offset: 1

Views

Author

Paolo P. Lava, Nov 27 2017

Keywords

Comments

4686 = 2*3*11*71.
All terms are multiples of a(1) = 70.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 289.

Examples

			Bernoulli B_{70} is 1505381347333367003803076567377857208511438160235/4686, hence 70 is in the sequence.

Links

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

  • Maple
    with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,4686);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 11, 71}:
select(filter, [seq(i, i=1..10^5)]);
  • Mathematica
    70 Position[Array[Denominator@ BernoulliB[70 #] &, 10^3], 4686][[All, 1]] (* Michael De Vlieger, Nov 27 2017 *)
Select[70*Range[750],Denominator[BernoulliB[#]]==4686&] (* Harvey P. Dale, Nov 23 2023 *)
  • PARI
    isok(n) = denominator(bernfrac(n)) == 4686; \\ Michel Marcus, Nov 27 2017
  • PARI
    lista(nn) = forstep(n=70, nn, 70, if(denominator(bernfrac(n)) == 4686, print1(n, ", "))) \\ Iain Fox, Nov 27 2017
Previous Showing 31-37 of 37 results.

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