A330519 Circulant determinant chain starting at 1007749

1007749, 18791108, -186878195, -1050017609, -9619142907, -4098030816, -59235488169, -43035664380, -25214990766, -189627605493, 779029018560, 14532890711040, 364989611366055, 1929185790836472, -1121729573175075, 13492031465869425, 329600773788765624

Offset

1,1

Comments

Form a circulant matrix from a given number. Find the determinant. Use that determinant to form the next circulant matrix. Repeat. If a determinant is negative, multiply each element of the next matrix by -1. 1007749 is the smallest number whose chain appears to increase without bound. (It would be nice to have a proof that this chain is unbounded!)

If we had started at 247, the next term in the chain, and all subsequent terms, would be 247, since (see A219324)

..........| 2 4 7 |

247 = det | 7 2 4 |. - N. J. A. Sloane, Dec 18 2019

..........| 4 7 2 |

Links

Jeff Heleen, Circulant determinant chain for 1007749: gives table of n, a(n) for n from 1 to 36.

N. J. A. Sloane, Recent and Noteworthy Sequences in the OEIS, Dec. 18, 2012

Crossrefs

Cf. A219324.

Sequence in context: A059925 A065327 A234035 * A066354 A220289 A133219

Adjacent sequences: A330516 A330517 A330518 * A330520 A330521 A330522

Keyword

sign,base

Author

Jeff Heleen, Dec 17 2019

Status

approved