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

1,1

Links

Table of n, a(n) for n=1..36.

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.

Example

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 ...
  ...

Crossrefs

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

Sequence in context: A290088 A179013 A090397 * A328729 A349441 A329733

Adjacent sequences: A339173 A339174 A339175 * A339177 A339178 A339179

Keyword

nonn,tabl,more

Author

Michel Marcus, Nov 26 2020

Status

approved