A076335 -id:A076335 - cp's OEIS frontend

A263561 Odd numbers n such that for every k >= 1, n*2^k - 1 has a divisor in the set {3, 5, 13, 17, 97, 241, 257}.

42270067, 97579567, 340716433, 721933559, 890948323, 1726122269, 1865978047, 1889699677, 2362339121, 3185721853, 3637126963, 4668508603, 5064217117, 5569622789, 7480754459, 7701804269, 8594194301, 9005098303, 9180863669, 9939496717, 9979211051

Offset: 1

Arkadiusz Wesolowski, Oct 21 2015

nonn

What is the smallest term of this sequence that belongs to A076335? Is it the smallest Brier number?

This sequence contains only numbers of the form 30*k + 7, 30*k + 11, 30*k + 13, 30*k + 29.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..96
Chris Caldwell, The Prime Glossary, Riesel number
Carlos Rivera, Problem 29 and Problem 58
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A076335, A263347.
Subsequence of A101036.
A263562 gives the primes.

a(n) = a(n-96) + 39832304070 for n > 96.

A291360 Prime divisors of 2^720 - 1.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 181, 241, 257, 331, 433, 577, 631, 673, 1321, 23311, 38737, 54001, 61681, 8369281, 18837001, 29247661, 394783681, 4278255361, 4562284561, 46908728641, 168692292721, 487824887233, 469775495062434961, 750016890283777055704738227247474485366338380663681

Offset: 1

Arkadiusz Wesolowski, Aug 23 2017

It is possible to find an odd positive integer k and a set S = {p(1), ..., p(s)} containing only primes which appeared in the sequence such that for any nonnegative integer n, k*2^n + 1 == 0 (mod p(i)) and k*2^n - 1 == 0 (mod p(j)) for some p(i) and some p(j) from the set S.

Index entries for sequences related to divisors of numbers

Cf. A076335, A154700. Supersequence of A269326.

Magma
```
PrimeDivisors(2^720-1);
```
Mathematica
```
Select[Divisors[2^720-1], PrimeQ]
```

forprime(p=1, , if(Mod(2, p)^720==1, print1(p, ", "))) \\ Felix Fröhlich, Aug 23 2017

A364412 Odd numbers m such that for every k >= 1, m*2^k - 1 has a divisor in the set {3, 7, 11, 19, 31, 37, 41, 61, 73, 109, 151, 331}.

Original entry on oeis.org

144323411864333, 175321252530209, 190779128601685, 316031956469111, 389882208980861, 450590081221877, 2420018284798363, 2715458757443051, 3161282469971861, 3366332338600025, 3643757921262355, 4380746955320089, 4409682697067321, 5089175909950511, 5281690092088615

Offset: 1

Arkadiusz Wesolowski, Jul 23 2023

nonn

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..34560

Cf. A101036, A076335, A180247, A291360, A364413.

For n > 34560, a(n) = a(n-34560) + 10014447295554878022.

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

A269326 Let k be a number which is simultaneously Sierpiński and Riesel, and let P be a set of primes which cover every number of the form k2^m + 1 and of the form k2^m - 1 with m >= 1. Sequence shows elements of the set P which has the property that the product of its primes is as small as it is possible.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257, 331

Offset: 1

Arkadiusz Wesolowski, Feb 23 2016

Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), pp. 79-81.

Cf. A076335, A076336, A101036.

PrimeDivisors((2^36-1)*(2^48-1)*(2^60-1))[1..18];

A281907 Numbers congruent to 47867742232066880047611079 modulo 66483034025018711639862527490.

Original entry on oeis.org

47867742232066880047611079, 66530901767250778519910138569, 133013935792269490159772666059, 199496969817288201799635193549, 265980003842306913439497721039, 332463037867325625079360248529, 398946071892344336719222776019, 465429105917363048359085303509

Offset: 1

Felix Fröhlich, Feb 01 2017

The terms of this sequence cannot be written as +-p^a +-q^b with p, q prime and a, b nonnegative integers for any possible choice of signs (cf. Theorem in Sun, 2000).

47867742232066880047611079 is a Brier number (A076335). - Jeppe Stig Nielsen, Sep 16 2020

Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comp. 29 (1975), 79-81.
Zhi-Wei Sun, On integers not of the form +-p^a+-q^b, Proceedings of the American Mathematical Society, Vol. 128, No. 4 (2000), 997-1002.

Cf. A153352.

Table[66483034025018711639862527490 n + 47867742232066880047611079, {n, 0, 7}] (* Michael De Vlieger, Feb 02 2017 *)

a(n) = 66483034025018711639862527490*n+47867742232066880047611079

a(n) = 66483034025018711639862527490*n + 47867742232066880047611079.

cp's OEIS Frontend

A263561 Odd numbers n such that for every k >= 1, n*2^k - 1 has a divisor in the set {3, 5, 13, 17, 97, 241, 257}.

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A291360 Prime divisors of 2^720 - 1.

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A364412 Odd numbers m such that for every k >= 1, m*2^k - 1 has a divisor in the set {3, 7, 11, 19, 31, 37, 41, 61, 73, 109, 151, 331}.

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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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Magma

A281907 Numbers congruent to 47867742232066880047611079 modulo 66483034025018711639862527490.

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