|
|
A223140
|
|
Decimal expansion of (sqrt(29) + 1)/2.
|
|
7
|
|
|
3, 1, 9, 2, 5, 8, 2, 4, 0, 3, 5, 6, 7, 2, 5, 2, 0, 1, 5, 6, 2, 5, 3, 5, 5, 2, 4, 5, 7, 7, 0, 1, 6, 4, 7, 7, 8, 1, 4, 7, 5, 6, 0, 0, 8, 0, 8, 2, 2, 3, 9, 4, 4, 1, 8, 8, 4, 0, 1, 9, 4, 3, 3, 5, 0, 0, 8, 3, 2, 2, 9, 8, 1, 4, 1, 3, 8, 2, 9, 3, 4, 6, 4, 3, 8, 3, 1, 6, 8, 9, 0, 8, 3, 9, 9, 1, 7, 7, 4, 2, 2, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Decimal expansion of sqrt(7 + sqrt(7 + sqrt(7 + sqrt(7 + ... )))).
Sequence with a(1) = 2 is decimal expansion of sqrt(7 - sqrt(7 - sqrt(7 - sqrt(7 - ... )))) - A223141.
This number phi29 = (1 + sqrt(29))/2 is the fundamental algebraic integer in the quadratic number field Q(sqrt(29)) with minimal polynomial x^2 - x - 7. The other root is -A223141.
phi29^n = 7*A(n-1) + A(n)*phi29, where A(n) = A015442(n) with A(-1) = 1/7, for n >= 0. For negative powers n see A367454 = 1/phi29. (End)
|
|
LINKS
|
|
|
FORMULA
|
sqrt(7 + sqrt(7 + sqrt(7 + sqrt(7 + ... )))) - 1 = sqrt(7 - sqrt(7 - sqrt(7 - sqrt(7 - ... )))). See A223141.
|
|
EXAMPLE
|
3.1925824035672520156253552457701...
|
|
MATHEMATICA
|
RealDigits[(1 + Sqrt[29])/2, 10, 130]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|