A257647 -id:A257647 - cp's OEIS frontend

A258154 Least k such that k2^m - 1 has a covering set of modulus 2n, or 0 if no such value exists.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 509203, 0, 0, 0, 0, 0, 777149, 0, 0, 0, 0, 0, 10157893, 0, 0, 0, 0, 0, 60014203, 0, 200883553191612793, 0, 0, 0, 7106977, 0, 0, 0

Offset: 1

Arkadiusz Wesolowski, Nov 05 2015

nonn

Wikipedia, Riesel number

Cf. A101036, A257647, A257861.

A270271 Odd numbers n such that for every k >= 1, n*2^k + 1 has a divisor in the set {3, 5, 17, 257, 641, 65537, 6700417}.

Original entry on oeis.org

201446503145165177, 1007236913771681629, 1697906240793858917, 2331023822106839599, 2935363331541925531, 3367034409844073483, 3914042604075779837, 4863495246870308311, 5036162578625852633, 5590196669446332863, 6705290764721718679, 7284449444083822547

Offset: 1

Arkadiusz Wesolowski, Mar 14 2016

nonn

M. Krizek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York, 2001, pp. 72-73.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..64
Chris Caldwell, The Prime Glossary, Sierpinski number
W. Sierpiński, Sur un problème concernant les nombres k * 2^n + 1, Elem. Math., 15 (1960), pp. 73-74.
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, 1, -1).

Cf. A257647. Subsequence of A076336.

lst:=[]; e:=2^64; P:=PrimeDivisors(e-1); C:=[1, 1, 1, 1, 1, 1, 33]; Pr:=&*[P[i]: i in [1..#P]]; S:=CRT([Modexp(2, C[i], P[i]): i in [1..#C]], P); for t in [1..33] do a:=S+Pr; g:=Gcd(a, e); S:=Floor(a/g); Append(~lst, S); end for; Sort(lst)[1..12];

a(n) = a(n-64) + 2*(2^64-1) for n > 64.

A289110 a(n) = number of covering sets of modulus 2*n for Sierpiński/Riesel numbers.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 23, 0, 1, 0, 0, 0

Offset: 1

Arkadiusz Wesolowski, Jun 24 2017

a(36) >= 93.

Note that it is not true that a(n) = 0 unless n is a multiple of 6. For example, a(40) = 1.

Yves Gallot, A search for some small Brier numbers, 2000.

Cf. A257647, A258154.

cp's OEIS Frontend

A258154 Least k such that k2^m - 1 has a covering set of modulus 2n, or 0 if no such value exists.

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A270271 Odd numbers n such that for every k >= 1, n*2^k + 1 has a divisor in the set {3, 5, 17, 257, 641, 65537, 6700417}.

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A289110 a(n) = number of covering sets of modulus 2*n for Sierpiński/Riesel numbers.

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Author

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cp's OEIS Frontend

A258154 Least k such that k*2^m - 1 has a covering set of modulus 2*n, or 0 if no such value exists.

Views

Author

Keywords

Links

Crossrefs

A270271 Odd numbers n such that for every k >= 1, n*2^k + 1 has a divisor in the set {3, 5, 17, 257, 641, 65537, 6700417}.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Magma

Formula

A289110 a(n) = number of covering sets of modulus 2*n for Sierpiński/Riesel numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

A258154 Least k such that k2^m - 1 has a covering set of modulus 2n, or 0 if no such value exists.