cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Chai Wah Wu, Oct 18 2021

Keywords

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

Examples

			           ⎡1  5  4  7⎤
1547 = det ⎢5  4  7  1⎥
           ⎢4  7  1  5⎥
           ⎣7  1  5  4⎦.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[10^6], Equal[Det[NestList[RotateLeft, #2, #3 - 1]], #1] & @@ {#1, #2, Length[#2]} & @@ {#, IntegerDigits[#]} &] (* Michael De Vlieger, Oct 18 2021 *)
  • 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
  • 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)