A160559 Minimal covering numbers.
12, 80, 90, 210, 280, 378, 448, 1386, 1650, 2200, 2464, 5346, 9750, 11264, 11466, 13000, 14994, 18954, 20384, 23166, 26656, 27846, 30294, 31122, 33150, 33858, 36608, 37050, 37674, 44200, 44850, 49400, 49504, 53248, 53900, 55328, 59800, 63750, 66976, 71250, 72930, 85000, 95000, 95744, 97240, 100100, 107008, 107406, 112112, 117306, 120042, 131274, 142002, 145314, 192500, 208544, 223074, 242250, 252448, 272272, 293250, 311168, 318500, 323000, 369750, 385434, 391000, 395250, 423500, 431250, 450846, 452608, 485982, 493000, 505856, 519498, 527000, 568458, 575000, 612352, 617526, 654500, 660114, 685216, 731500, 735150, 747954
Offset: 1
Keywords
Examples
80 is in the set since 1 mod 2; 2 mod 4; 4 mod 8; 8 mod 16; 4 mod 5; 8 mod 10; 16 mod 20, 32 mod 40; 0 mod 80 is a covering system with LCM 80. None of the divisors has that property. 36 is not minimal since 12 is a divisor and 12 is the LCM of a covering system.
Links
- Jai Setty, Table of n, a(n) for n = 1..87
- Max Alekseyev, Covering systems corresponding to the terms a(1)-a(41).
- Donald Jason Gibson, A covering system with least modulus 25, Math. Comp. 78 (2009), 1127-1146.
- Robert D. Hough and Pace P. Nielsen, Covering systems with restricted divisibility, Duke Math. J. 168:17 (2019), 3261-3295. arXiv:1703.02133 [math.NT].
- Pace P. Nielsen, A covering system whose smallest modulus is 40, Journal of Number Theory 129 (2009), 640-666.
- Pace P. Nielsen, A movie explaining covering systems.
- Jai Setty, Covering systems corresponding to the terms a(1)-a(87).
Crossrefs
Cf. A160560.
Extensions
Corrected by Eric Rowland, Oct 24 2018
a(17)-a(23) from Max Alekseyev, Nov 19 2022
a(24)-a(41) from Max Alekseyev, Mar 21 2023
Missing terms a(8) and a(15) inserted and their multiples removed by Jai Setty, May 29 2024
Comments