A076337 -id:A076337 - cp's OEIS frontend

A373804 Primes in A374965 sorted into increasing order.

3, 19, 103, 283, 313, 331, 463, 733, 751, 757, 1093, 1153, 1213, 1453, 1543, 1783, 2083, 2251, 2371, 2467, 2671, 2707, 2803, 3733, 3823, 7603, 7723, 8221, 9013, 9661, 14983, 15277, 15607, 16363, 16381, 16843, 17923, 19483, 20287, 21061, 22093, 23173, 24421, 24841, 25903, 27211, 28411

Offset: 1

N. J. A. Sloane, Aug 08 2024

nonn

Since we know the first 350199 terms of A374965, and A374965(350199) = 5026186 starts a new doubling chain, we know that any subsequent prime is greater than 5026186. This implies that the terms in the b-file, which are < 5026186, are correct. Of course, if the sequence reaches a Riesel number (cf. A076337) there will be no more primes after that point.

Note that, as can be seen from the b-file in A375028, A374965 contains many primes greater than 5026186 among the first 350199 terms, including one prime with 102410 digits. But these large primes cannot be added to the present b-file until more is discovered about primes following term 350199.

N. J. A. Sloane, Table of n, a(n) for n = 1..184
N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Cf. A374965, A375028, A373799, A076337.

A177331 Prime numbers p such that (p*2^k-1)/3 is composite for all even k or all odd k.

Original entry on oeis.org

557, 743, 919, 1163, 3257, 3301, 4817, 5209, 5581, 6323, 6421, 6983, 7457, 7793

Offset: 1

T. D. Noe, May 08 2010

nonn

This sequence consists of the primes >3 for which A177330 is zero. k is even when p=1 (mod 6); k is odd when p=5 (mod 6). This problem is similar to that of finding Sierpinski and Riesel numbers (see A076336 and A076337). Compositeness of (p*2^k-1)/3 for all even or all odd k is established by finding a finite set of primes such that at least one member of the set divides each term. For p <= 7797, the set of primes is {3,5,7,13}.

A236321 Conjectured number of Riesel numbers less than 10^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 5, 65, 668, 6711

Offset: 1

Arkadiusz Wesolowski, Jan 22 2014

Wikipedia, Riesel number

Cf. A076337, A101036, A236320, A237880.

a(n) ~ A236320(n).

A237880 Conjectured number of distinct integers < 10^n that are Sierpiński or Riesel or simultaneously Sierpiński and Riesel numbers.

Original entry on oeis.org

0, 0, 0, 0, 1, 16, 134, 1345, 13420

Offset: 1

Arkadiusz Wesolowski, Feb 14 2014

Wikipedia, Riesel number
Wikipedia, Sierpinski number

Cf. A076335, A076336, A076337, A101036, A236320, A236321.

a(n) = A236320(n) + A236321(n) for n <= 9.

Definition clarified by Arkadiusz Wesolowski, Jun 05 2021

A273987 Smallest Riesel number to base n.

Original entry on oeis.org

509203, 63064644938, 9, 346802, 84687, 408034255082, 14, 4, 10176, 862, 25, 302, 4, 36370321851498, 9, 86, 246, 144, 8, 560, 4461, 476, 4, 36, 149, 8, 144, 4, 1369, 134718, 10, 16, 6, 287860, 4, 7772, 13, 4, 81, 8, 15137, 672, 4, 22564, 8177, 14, 3226, 36, 16

Offset: 2

Tim Johannes Ohrtmann, Jun 06 2016

a(2), a(3), a(5), a(6), a(7), a(10), a(15), a(22), a(23), a(30), ... are only conjectural (see links).

Gary Barnes, Riesel conjectures and proofs.
Gary Barnes, Riesel conjectures and proofs, Powers of 2.
Gary Barnes, Condensed table of all conjectures for bases ≤ 1030.
Wikipedia, Riesel number.

Cf. A076337, A101036.

A085917 Least k such that k*2^n - 1 is a semiprime.

Original entry on oeis.org

5, 4, 2, 1, 3, 5, 4, 2, 1, 2, 1, 3, 6, 3, 3, 3, 3, 6, 3, 3, 3, 2, 1, 3, 6, 3, 6, 3, 6, 3, 3, 11, 16, 8, 4, 2, 1, 8, 4, 2, 1, 15, 13, 15, 16, 8, 4, 2, 1, 6, 3, 17, 15, 12, 6, 3, 4, 2, 1, 3, 6, 3, 3, 5, 3, 2, 1, 5, 6, 3, 48, 24, 12, 6, 3, 12, 6, 3, 10, 5, 4, 2, 1, 3, 3, 31, 21, 17, 15, 11, 13, 24, 12, 6, 3

Offset: 1

Jason Earls, Aug 16 2003

nonn

The first few values of n such that 509203*2^n - 1 is a semiprime, where k = 509203 (the conjectured smallest Riesel number), are: 3,4,16,34,61,82,124,142,163,171,... Conjecture: there are infinitely many semiprimes of this form.

			a(33)=16 because k*2^33 - 1 is not a semiprime for k=1,2,...15, but 16*2^33 - 1 = 223 * 616318177 is.

Sean A. Irvine, Table of n, a(n) for n = 1..500

Cf. A001358, A085427, A076337, A085245.

A206430 Least k such that k*2^m - 1 has a covering set with precisely n primes.

Original entry on oeis.org

509203, 777149, 7106977, 60014203

Offset: 6

Arkadiusz Wesolowski, Apr 19 2012

A set of primes is a covering set for k*2^m - 1 if for every positive integer m there is some prime in the set which divides k*2^m - 1. Only minimal covering sets are considered here (those which would not remain covering sets with the removal of any element).

			509203 has the covering set {3, 5, 7, 13, 17, 241}.
777149 has the covering set {3, 5, 7, 13, 19, 37, 73}.
7106977 has the covering set {3, 5, 13, 17, 19, 109, 241, 433}.
60014203 has the covering set {3, 5, 7, 11, 13, 31, 41, 61, 151}.

Wikipedia, Covering set
Wikipedia, Riesel number

Cf. A076337, A101036.

A244545 Integers n such that for every integer k>0, n*6^k+1 has a divisor in the set { 7, 13, 31, 37, 43 }.

Original entry on oeis.org

243417, 1161910, 1293662, 1434861, 1446213, 1460502, 1473746, 1689722, 2284675, 2483249, 2485141, 2693347, 2695449, 2708061, 2783733, 3207751, 3237765, 3273761, 3684535, 4120955, 4154366, 4189067, 4274801, 4354265

Offset: 1

Pierre CAMI, Jun 29 2014

nonn

For n > 24, a(n) = a(n-24) + 4488211, 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 always has 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) + 4488211.

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.

cp's OEIS Frontend

A373804 Primes in A374965 sorted into increasing order.

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A177331 Prime numbers p such that (p*2^k-1)/3 is composite for all even k or all odd k.

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A236321 Conjectured number of Riesel numbers less than 10^n.

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A237880 Conjectured number of distinct integers < 10^n that are Sierpiński or Riesel or simultaneously Sierpiński and Riesel numbers.

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A273987 Smallest Riesel number to base n.

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A085917 Least k such that k*2^n - 1 is a semiprime.

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A206430 Least k such that k*2^m - 1 has a covering set with precisely n primes.

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A244545 Integers n such that for every integer k>0, n*6^k+1 has a divisor in the set { 7, 13, 31, 37, 43 }.

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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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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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