|
| |
|
|
A086403
|
|
Numerators in continued fraction representation of (e-1)/(e+1).
|
|
0
| |
|
|
1, 6, 61, 860, 15541, 342762, 8927353, 268163352, 9126481321, 347074453550, 14586253530421, 671314736852916, 33580323096176221, 1814008761930368850, 105246088515057569521, 6527071496695499679152, 430891964870418036393553, 30168964612425958047227862
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| Calvin C. Clawson, "Mathematical Mysteries", Perseus, 1999, p. 225.
|
|
|
FORMULA
| Partial quotients in continued fraction representation of (e-1)/(e+1) are A016825: [2, 6, 10, 14, 18...], the convergents being: [2] = 1/2, [2, 6] = 6/13, [2, 6, 10] = 61/132...etc.; denominators are A079165 starting with n=1: 2, 13, 132, 1861, 33630, 741721, 19318376... 2. a(n) = closest integer to [(e-1)/(e+1)]*A079165(n), n>0
|
|
|
EXAMPLE
| a(4) = 860 = closest integer to[(e-1)/(e+1)]*A079165(4); = floor(860.0000292...) = 860. 860/1861 = [2, 6, 10, 14] = .462117141...; (e-1)/(e+1) = .462117157...
|
|
|
MAPLE
| b:= proc(n) local i, q;
q:= 0;
for i to n do
q:= 1/(q+4*(n-i)+2)
od; q
end:
a:= n-> numer (b(n)):
seq (a(n), n=1..20); # Alois P. Heinz, Feb 03 2012
|
|
|
CROSSREFS
| Cf. A016825, A079165.
Sequence in context: A064088 A191803 A047737 * A049120 A056546 A127695
Adjacent sequences: A086400 A086401 A086402 * A086404 A086405 A086406
|
|
|
KEYWORD
| nonn,changed
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 18 2003
|
|
|
EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 03 2012
|
| |
|
|
