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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.
0
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
1,2
COMMENTS
A left circulant matrix is also called a anti-circulant or (-1)-circulant matrix.
Subsequence of A219327.
Fixed points of A177894. - John Keith, Oct 24 2021
EXAMPLE
⎡1 5 4 7⎤
1547 = det ⎢5 4 7 1⎥
⎢4 7 1 5⎥
⎣7 1 5 4⎦.
MATHEMATICA
Select[Range[10^6], Equal[Det[NestList[RotateLeft, #2, #3 - 1]], #1] & @@ {#1, #2, Length[#2]} & @@ {#, IntegerDigits[#]} &] (* Michael De Vlieger, Oct 18 2021 *)
PROG
(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)
(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
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Chai Wah Wu, Oct 18 2021
STATUS
approved