|
| |
|
|
A351898
|
|
Decimal expansion of metallic ratio for N = 14.
|
|
0
|
|
|
|
1, 4, 0, 7, 1, 0, 6, 7, 8, 1, 1, 8, 6, 5, 4, 7, 5, 2, 4, 4, 0, 0, 8, 4, 4, 3, 6, 2, 1, 0, 4, 8, 4, 9, 0, 3, 9, 2, 8, 4, 8, 3, 5, 9, 3, 7, 6, 8, 8, 4, 7, 4, 0, 3, 6, 5, 8, 8, 3, 3, 9, 8, 6, 8, 9, 9, 5, 3, 6, 6, 2, 3, 9, 2, 3, 1, 0, 5, 3, 5, 1, 9, 4, 2, 5, 1, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
2,2
|
|
|
COMMENTS
|
Decimal expansion of continued fraction [14; 14, 14, 14, ...].
Also largest solution of x^2 - 14 x - 1 = 0.
Essentially the same digit sequence as A010503, A157214, A174968 and A268683.
The metallic ratio's for N = A077444(n) are equal to powers of the silver ratio, i.e., A014166^(2n-1); this constant represents the special case for N = A077444(2).
|
|
|
LINKS
|
Table of n, a(n) for n=2..88.
Michael Penn, 7+5√2 is a perfect cube??, YouTube video, 2022.
Wikipedia, Metallic mean.
|
|
|
FORMULA
|
Equals 2 + 5*A014176.
Equals A014176^3.
|
|
|
EXAMPLE
|
14.0710678118654752440084436210484903928483593...
|
|
|
MATHEMATICA
|
RealDigits[7 + 5*Sqrt[2], 10, 100][[1]] (* Amiram Eldar, Feb 24 2022 *)
|
|
|
PROG
|
(PARI) (1+sqrt(2))^3
|
|
|
CROSSREFS
|
Cf. A010503, A077444, A157214, A174968, A268683.
Metallic ratios: A001622 (N=1), A014176 (N=2), A098316 (N=3), A098317 (N=4), A098318 (N=5), A176398 (N=6), A176439 (N=7), A176458 (N=8), A176522 (N=9), A176537 (N=10), A244593 (N=11).
Sequence in context: A052400 A354450 A199071 * A157698 A342360 A251967
Adjacent sequences: A351895 A351896 A351897 * A351899 A351900 A351901
|
|
|
KEYWORD
|
nonn,cons
|
|
|
AUTHOR
|
A.H.M. Smeets, Feb 24 2022
|
|
|
STATUS
|
approved
|
| |
|
|
