A200141 Upper bound by J. Rivat and J. Wu on constant arising in Piatetski-Shapiro primes.

1, 1, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5, 3, 6, 5, 8, 5

Offset

1,3

Comments

Xi proves a quantitative version of the statement that every nonempty finite subset of N+ is a set of quadratic residues for infinitely many primes of the form [n^c] with 1 <= c <= 243/205.

Links

Table of n, a(n) for n=1..99.

Victor Zhenyu Guo, Jinjiang Li and Min Zhang, Piatetski-Shapiro primes in the intersection of multiple Beatty sequences, arXiv:2109.00461 [math.NT], 2021.

Ping Xi, Quadratic residues and non-residues for infinitely many Piatetski-Shapiro primes, arXiv:1111.2641 [math.NT], 2011-2012.

Formula

243/205.

Example

1.18536585...

Crossrefs

Sequence in context: A086723 A011406 A201488 * A011466 A154509 A081885

Adjacent sequences: A200138 A200139 A200140 * A200142 A200143 A200144

Keyword

nonn,easy,cons

Author

Jonathan Vos Post, Nov 13 2011

Status

approved