A348428 - OEIS

%I #22 Oct 24 2021 11:22:55

%S 1,2,3,4,5,6,7,8,9,1547,26027,26933,45018,69781,80487,154791,23203827,

%T 257059332,278945612,456790123,469135802,493827160,494376160,

%U 506172839,530864197,543209876,897163795,1662971175,2293668391,3880266075,6473710191

%N Positive integers m that are equal to the determinant of the left circulant matrix formed by the decimal digits of m.

%C A left circulant matrix is also called a anti-circulant or (-1)-circulant matrix.

%C Subsequence of A219327.

%C Fixed points of A177894. - _John Keith_, Oct 24 2021

%e            ⎡1  5  4  7⎤

%e 1547 = det ⎢5  4  7  1⎥

%e            ⎢4  7  1  5⎥

%e            ⎣7  1  5  4⎦.

%t Select[Range[10^6], Equal[Det[NestList[RotateLeft, #2, #3 - 1]], #1] & @@ {#1, #2, Length[#2]} & @@ {#, IntegerDigits[#]} &] (* _Michael De Vlieger_, Oct 18 2021 *)

%o (Python)

%o from sympy import Matrix

%o A348428_list = []

%o for n in range(1,10**6):

%o     s = [int(d) for d in str(n)]

%o     m = len(s)

%o     if n == Matrix(m, m, lambda i, j: s[(i+j) % m]).det():

%o         A348428_list.append(n)

%o (PARI) isok(m) = {my(d=digits(m), x); matdet(matrix(#d, #d, i, j, if (i==1, d[j], x = lift(Mod(j+i-1, #d)); if (!x, x += #d); d[x]))) == m;} \\ _Michel Marcus_, Oct 19 2021

%Y Cf. A219324, A219326, A219327.

%Y Cf. A177894.

%K nonn,base,more

%O 1,2

%A _Chai Wah Wu_, Oct 18 2021