A244070 -id:A244070 - cp's OEIS frontend

A244924 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set { 3, 5, 7, 13, 17, 97, 673 }.

73520771, 108288041, 127499219, 141239113, 160792529, 198545797, 205293103, 217763051, 227258803, 262056089, 269931509, 303224819, 307060289, 353982553, 368427809, 430034677, 525141899, 581603107, 585721991, 600824113, 612314921, 644606467, 718519237, 723522461

Offset: 1

Pierre CAMI, Jul 08 2014

nonn

For n > 96 a(n) = a(n-96) + 3029691210, the first 96 values are given in the table.

Pierre CAMI, Table of n, a(n) for n = 1..96

Cf. A244070, A244071, A244072, A244073, A244074, A244076.

For n > 96 a(n)=a(n-96) + 3029691210

A271027 a(n) = 3661529 + 11184810*n.

Original entry on oeis.org

3661529, 14846339, 26031149, 37215959, 48400769, 59585579, 70770389, 81955199, 93140009, 104324819, 115509629, 126694439, 137879249, 149064059, 160248869, 171433679, 182618489, 193803299, 204988109, 216172919, 227357729, 238542539, 249727349, 260912159, 272096969, 283281779, 294466589

Offset: 0

Altug Alkan, Mar 29 2016

a(n) and a(n) + 14 are the members of A101036.

14 appears as a minimum difference between Riesel numbers for the first 15000 terms that are listed in b-file of A101036.

			a(1) = 3661529 + 11184810*1 = 14846339.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A101036, A244070, A270993.

[3661529 + 11184810*n : n in [0..40]]; // Wesley Ivan Hurt, Apr 02 2016

A271027:=n->3661529 + 11184810*n: seq(A271027(n), n=0..40); # Wesley Ivan Hurt, Apr 02 2016

CoefficientList[Series[(3661529 + 7523281 x)/(1 - x)^2, {x, 0, 26}], x] (* Michael De Vlieger, Mar 29 2016 *)
LinearRecurrence[{2,-1},{3661529,14846339},30] (* Harvey P. Dale, Sep 10 2019 *)

PARI
```
a(n) = 3661529 + 11184810*n;
```

x='x+O('x^99); Vec((3661529+7523281*x)/(1-x)^2)

for n in range(0,100):print(3661529+11184810*n) # Soumil Mandal, Apr 03 2016

G.f.: (3661529 + 7523281*x)/(1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>1.

A244351 Integers n such that for every integer k>0, n*6^k-1 has a divisor in the set { 7, 13, 31, 37, 97 }.

Original entry on oeis.org

84687, 429127, 508122, 1273238, 1570311, 1656045, 2574762, 2847748, 3048732, 3345805, 3849481, 5076399, 5324003, 5338292, 5908351, 6961919, 7639428, 8167823, 8508662, 8994775, 9078721, 9421866, 9936270, 9950261

Offset: 1

Pierre CAMI, Jun 26 2014

nonn

For n > 24 a(n) = a(n-24) + 10124569, the first 24 values are in the data.

When the number a(n) has 1 or 6 as the last digit the number a(n)*6^k-1 is always divisible by 5 and have always a divisor in the set { 7, 13, 31, 37, 97 } for every k.

Cf. A076337, A243969, A244070, A244071, A244072, A244073, A244074, A244076, A244211.

For n>24 a(n) = a(n-24) + 10124569.

A244549 Integers m such that for every integer k>0, m*6^k+1 has a divisor in the set { 7, 13, 31, 37, 97 }.

Original entry on oeis.org

174308, 188299, 702703, 1045848, 1129794, 1615907, 1956746, 2485141, 3162650, 4216218, 4786277, 4800566, 5048170, 6275088, 6778764, 7075837, 7276821, 7549807, 8468524, 8554258, 8851331, 9616447, 9695442, 10039882

Offset: 1

Pierre CAMI, Jun 29 2014

nonn

For n > 24 a(n) = a(n-24) + 10124569, the first 24 values are in the data.

When the number a(n) has 4 or 9 as the last digit the number a(n)*6^k-1 is always divisible by 5 and have always a divisor in the set { 7, 13, 31, 37, 97 } for every k.

Cf. A076337, A243969, A244070, A244071, A244072, A244073, A244074, A244076, A244211, A244545.

For n > 24 a(n) = a(n-24) + 10124569.

A345685 a(n) is the smallest cardinality of all covering sets associated with Riesel number A101036(n).

Original entry on oeis.org

6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6

Offset: 1

Felix Fröhlich, Jun 23 2021

The condition for choosing a covering set is necessary as there are Riesel numbers with more than one covering set, see A263392.

			   n | Riesel number | Covering set               | a(n)
--------------------------------------------------------
   1 |  509203       | {3, 5, 7, 13, 17, 241}     | 6
   2 |  762701       | {3, 5, 7, 13, 17, 241}     | 6
   3 |  777149       | {3, 5, 7, 13, 19, 37, 73}  | 7
   4 |  790841       | {3, 5, 7, 13, 19, 37, 73}  | 7
   5 |  992077       | {3, 5, 7, 13, 17, 241}     | 6
   6 | 1106681       | {3, 5, 7, 13, 19, 37, 73}  | 7
   7 | 1247173       | {3, 5, 7, 13, 17, 241}     | 6
   8 | 1254341       | {3, 5, 7, 13, 17, 241}     | 6
   9 | 1330207       | {3, 5, 7, 13, 17, 241}     | 6
  10 | 1330319       | {3, 5, 7, 13, 17, 241}     | 6
  11 | 1715053       | {3, 5, 7, 13, 19, 37, 73}  | 7
  12 | 1730653       | {3, 5, 7, 13, 17, 241}     | 6
  13 | 1730681       | {3, 5, 7, 13, 17, 241}     | 6
  14 | 1744117       | {3, 5, 7, 13, 19, 73, 109} | 7
  15 | 1830187       | {3, 5, 7, 13, 37, 73, 109} | 7
  16 | 1976473       | {3, 5, 7, 13, 17, 241}     | 6

Prime Wiki, Category:Riesel k=Riesel [Links to pages giving the covering sets of Riesel numbers]
Wikipedia, Riesel number

Cf. A101036, A244070, A244071, A244072, A244073, A244074, A263392.

cp's OEIS Frontend

A244924 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set { 3, 5, 7, 13, 17, 97, 673 }.

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A271027 a(n) = 3661529 + 11184810*n.

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A244351 Integers n such that for every integer k>0, n*6^k-1 has a divisor in the set { 7, 13, 31, 37, 97 }.

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Author

Keywords

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Formula

A244549 Integers m such that for every integer k>0, m*6^k+1 has a divisor in the set { 7, 13, 31, 37, 97 }.

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Author

Keywords

Comments

Crossrefs

Formula

A345685 a(n) is the smallest cardinality of all covering sets associated with Riesel number A101036(n).

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