A339176 - OEIS

%I #14 Jan 16 2024 18:29:23

%S 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,

%T 8707,4040,632,2,19,262,8340,66740,336957,51353,2752

%N 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.

%H Bruce Dearden and Jerry Metzger, <a href="https://doi.org/10.1006/eujc.1996.0124">Roots of Polynomials Modulo Prime Powers</a>, European Journal of Combinatorics, Volume 18, Issue 6, August 1997, Pages 601-606.

%H Aditya Gulati, Sayak Chakrabarti, and Rajat Mittal, <a href="https://arxiv.org/abs/2011.10978">On algorithms to find p-ordering</a>, arXiv:2011.10978 [math.NT], 2020.

%H Davesh Maulik, <a href="https://doi.org/10.1006/jcta.2000.3069">Root Sets of Polynomials Modulo Prime Powers</a>, J. Comb. Theory, Ser. A, 93:125-140, 01 2001.

%F T(n,1) = 2; T(n,2) = prime(n)+2.

%F 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.

%e The array begins:

%e     k | 1 2  3    4 ...

%e   ---------------------

%e   p=2 | 2 4  8   20 ...

%e   p=3 | 2 5 17   71 ...

%e   p=5 | 2 7 42  427 ...

%e   p=7 | 2 9 79 1486 ...

%e   ...

%Y Cf. A007395 (column 1), A052147 (column 2).

%K nonn,tabl,more

%O 1,1

%A _Michel Marcus_, Nov 26 2020