A263392 -id:A263392 - cp's OEIS frontend

A263391 Sierpiński numbers that have at least two covering sets.

12151397, 31210219, 45181667, 56191673, 66887071, 68468753, 69169397, 71307347, 114921271, 122311103, 133228283, 152252267, 154337567, 182479909, 185282537, 192413177, 210465533, 220192013, 226521259, 235663343, 236281883, 253282909, 275248343, 282777829

Offset: 1

Arkadiusz Wesolowski, Oct 16 2015

nonn

			For every k >= 1, 12151397*2^k + 1 has a divisor in the set {3, 5, 7, 13, 19, 37, 73} and also in the set {3, 5, 7, 13, 19, 73, 109}. 12151397 is therefore in the sequence.

Wikipedia, Sierpinski number

Cf. A076336, A263392.

2 terms inserted by Arkadiusz Wesolowski, Aug 28 2016

More terms from Arkadiusz Wesolowski, Jan 09 2018

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

A263391 Sierpiński numbers that have at least two covering sets.

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