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A348428 Positive integers m that are equal to the determinant of the left circulant matrix formed by the decimal digits of m.

%I A348428 #22 Oct 24 2021 11:22:55
%S A348428 1,2,3,4,5,6,7,8,9,1547,26027,26933,45018,69781,80487,154791,23203827,
%T A348428 257059332,278945612,456790123,469135802,493827160,494376160,
%U A348428 506172839,530864197,543209876,897163795,1662971175,2293668391,3880266075,6473710191
%N A348428 Positive integers m that are equal to the determinant of the left circulant matrix formed by the decimal digits of m.
%C A348428 A left circulant matrix is also called a anti-circulant or (-1)-circulant matrix.
%C A348428 Subsequence of A219327.
%C A348428 Fixed points of A177894. - _John Keith_, Oct 24 2021
%e A348428            ⎡1  5  4  7⎤
%e A348428 1547 = det ⎢5  4  7  1⎥
%e A348428            ⎢4  7  1  5⎥
%e A348428            ⎣7  1  5  4⎦.
%t A348428 Select[Range[10^6], Equal[Det[NestList[RotateLeft, #2, #3 - 1]], #1] & @@ {#1, #2, Length[#2]} & @@ {#, IntegerDigits[#]} &] (* _Michael De Vlieger_, Oct 18 2021 *)
%o A348428 (Python)
%o A348428 from sympy import Matrix
%o A348428 A348428_list = []
%o A348428 for n in range(1,10**6):
%o A348428     s = [int(d) for d in str(n)]
%o A348428     m = len(s)
%o A348428     if n == Matrix(m, m, lambda i, j: s[(i+j) % m]).det():
%o A348428         A348428_list.append(n)
%o A348428 (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 A348428 Cf. A219324, A219326, A219327.
%Y A348428 Cf. A177894.
%K A348428 nonn,base,more
%O A348428 1,2
%A A348428 _Chai Wah Wu_, Oct 18 2021