A351021 - OEIS

%I #19 Oct 13 2022 06:48:54

%S 1,2,13,166,4009,169469,10949857,1078348288,138679521597,

%T 24402542896843,5348124003487173

%N Minimal permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A351021%2B2.sage">A351021+2.sage</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>

%e a(3) = 166:

%e     3    2    5

%e     2    3    2

%e     5    2    3

%e a(4) = 4009:

%e     3    2    5    7

%e     2    3    2    5

%e     5    2    3    2

%e     7    5    2    3

%e a(5) = 169469:

%e     5    2    3    7   11

%e     2    5    2    3    7

%e     3    2    5    2    3

%e     7    3    2    5    2

%e    11    7    3    2    5

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix, prime

%o def A351021(n): return 1 if n == 0 else min(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).per() for p in permutations(prime(i) for i in range(1,n+1))) # _Chai Wah Wu_, Jan 31 2022

%Y Cf. A348891, A350939, A350955, A351022 (maximal).

%K nonn,hard,more

%O 0,2

%A _Stefano Spezia_, Jan 29 2022

%E a(9) and a(10) from _Lucas A. Brown_, Sep 04 2022