A339176 Square array read by rising antidiagonals. T(n, k) is the k-th root of the number of root sets modulo p the n-th prime.
2, 2, 4, 2, 5, 8, 2, 7, 17, 20, 2, 9, 42, 71, 56, 2, 13, 79, 427, 449, 184, 2, 15, 189, 1486, 8707, 4040, 632, 2, 19, 262, 8340, 66740, 336957, 51353, 2752
Offset: 1
Examples
The array begins:
k | 1 2 3 4 ...
---------------------
p=2 | 2 4 8 20 ...
p=3 | 2 5 17 71 ...
p=5 | 2 7 42 427 ...
p=7 | 2 9 79 1486 ...
...
Links
- Bruce Dearden and Jerry Metzger, Roots of Polynomials Modulo Prime Powers, European Journal of Combinatorics, Volume 18, Issue 6, August 1997, Pages 601-606.
- Aditya Gulati, Sayak Chakrabarti, and Rajat Mittal, On algorithms to find p-ordering, arXiv:2011.10978 [math.NT], 2020.
- Davesh Maulik, Root Sets of Polynomials Modulo Prime Powers, J. Comb. Theory, Ser. A, 93:125-140, 01 2001.
Formula
T(n,1) = 2; T(n,2) = prime(n)+2.
T(n,3) = (3*p^2+p+4)/2 and T(n,4) = (3*p^4+4*p^3+6*p^2+5*p+12)/6, both where p>2 is the n-th prime. See Gulati et al.