A219357 a(n) = smallest number greater than n, equal to the determinant of the circulant matrix formed by its base-n digits.

17298, 1352, 28, 28, 320, 81, 133, 104, 247, 126, 1273, 252, 793, 473, 520, 980, 832, 513, 468, 5792, 684, 1738, 2511, 684, 1520, 14711, 7588, 938, 3857, 2275, 4680, 13392, 5184, 1648, 10535, 1820, 9143, 8473, 3843, 21880, 11609, 3843

Offset

2,1

Comments

Trivially all one-digit matrices are solutions, which is why 'greater than n' is specified. Two-digit matrices can never be a solution, so entries are actually greater than n^2. Most terms are three-digit solutions (less than n^3). Known exceptions are 15 digits (base 2), 7 digits (base 3), and 4 digits (bases 6, 798, 1182).

Up to base 1200, coincident terms are 28, 684, 3843, 8190, 47664, 80199, 351819, 323505, 5879259, 601524, 17159660, 20777715, respectively for base pairs (4,5), (22,25), (40,43), (81,86), (94,97), (112,115), (184,187), (276,386), (472,475), (738,749), (1061,1066), (1131,1136).

Links

Hans Havermann, Table of n, a(n) for n = 2..1200

Hans Havermann, log plot to base 1200

Eric W. Weisstein, MathWorld: Circulant Matrix

Example

In A219325 (base 2), the smallest number greater than 2 is 17298.
In A219324 (base 10), the smallest number greater than 10 is 247.

Mathematica

dcm[n_, b_] := (l = IntegerDigits[n, b]; Det[NestList[RotateRight, l, Length[l]-1]]); Table[i=b; While[dcm[i, b] != i, i++]; i, {b, 2, 43}]

Crossrefs

Cf. A219324 (base 10), A219325 (base 2).

Sequence in context: A228379 A230164 A001381 * A219325 A255780 A023942

Adjacent sequences: A219354 A219355 A219356 * A219358 A219359 A219360

Keyword

nonn,base

Author

Hans Havermann, Nov 18 2012

Status

approved