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

1,2

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

Links

Table of n, a(n) for n=1..31.

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

Cf. A219324, A219326, A219327.

Cf. A177894.

Sequence in context: A032563 A223081 A077727 * A032557 A282782 A032565

Adjacent sequences: A348425 A348426 A348427 * A348429 A348430 A348431

Keyword

nonn,base,more

Author

Chai Wah Wu, Oct 18 2021

Status

approved