A219327 Positive integers k that are equal to the absolute value of the determinant of the circulant matrix formed by the decimal digits of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 48, 247, 370, 378, 407, 481, 518, 592, 629, 1360, 1547, 3075, 26027, 26933, 45018, 69781, 80487, 123823, 154791, 289835, 1920261, 2137616, 2716713, 3100883, 3480140, 3934896, 4179451, 4830936, 5218958, 11955168, 23203827, 80651025, 95738203

Offset: 1

Author

Max Alekseyev, Nov 17 2012

Keywords

• base
• nonn

Comments

Contains A219324 and A219326 as subsequences.

Equal to the sequence defined by replacing circulant matrices with left circulant matrices. - Chai Wah Wu, Oct 18 2021

Links

• Robert G. Wilson v and Max Alekseyev, Table of n, a(n) for n = 1..63 (complete up to 10^10)

Crossrefs

A219324, the main entry for this sequence, provides references and further details.

Cf. A219326.

Programs

Python

from sympy import Matrix
A219327_list = []
for n in range(1,10**6):
    s = [int(d) for d in str(n)]
    m = len(s)
    if n == abs(Matrix(m, m, lambda i, j: s[(i-j) % m]).det()):
        A219327_list.append(n) # Chai Wah Wu, Oct 18 2021

Extensions

a(53)-a(63) from Max Alekseyev, Feb 15 2013