A348428 Positive integers m that are equal to the determinant of the left circulant matrix formed by the decimal digits of m.
1, 2, 3, 4, 5, 6, 7, 8, 9, 1547, 26027, 26933, 45018, 69781, 80487, 154791, 23203827, 257059332, 278945612, 456790123, 469135802, 493827160, 494376160, 506172839, 530864197, 543209876, 897163795, 1662971175, 2293668391, 3880266075, 6473710191
Offset: 1
Examples
⎡1 5 4 7⎤ 1547 = det ⎢5 4 7 1⎥ ⎢4 7 1 5⎥ ⎣7 1 5 4⎦.
Programs
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Mathematica
Select[Range[10^6], Equal[Det[NestList[RotateLeft, #2, #3 - 1]], #1] & @@ {#1, #2, Length[#2]} & @@ {#, IntegerDigits[#]} &] (* Michael De Vlieger, Oct 18 2021 *)
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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
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Python
from sympy import Matrix A348428_list = [] for n in range(1,10**6): s = [int(d) for d in str(n)] m = len(s) if n == Matrix(m, m, lambda i, j: s[(i+j) % m]).det(): A348428_list.append(n)
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