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

Author

Jonathan Vos Post, Nov 13 2011

Keywords

• nonn
• easy
• cons

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.

Examples

			1.18536585...
		

Links

• 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.