|
|
A219357
|
|
a(n) = smallest number greater than n, equal to the determinant of the circulant matrix formed by its base-n digits.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|