|
Search: id:A084909
|
|
|
| A084909 |
|
Indices of Fibonacci numbers that satisfy: sum(n>=1,1/F(a(n)))=tau-1, where F(k) gives the k-th Fibonacci number with F(0)=1, such that the partial sums are nearest to, but never exceed, tau-1=(sqrt(5)-1)/2. |
|
+0
3
|
|
| 2, 6, 8, 10, 17, 21, 24, 26, 29, 34, 42, 46, 49, 51, 54, 56, 59, 61, 63, 65, 67, 69, 71, 77, 79, 81, 85, 88, 90, 92, 94, 101, 103, 110, 114, 121, 123, 129, 131, 134, 137, 143, 146, 149, 154, 156, 160, 163, 167, 172, 176, 181, 183, 185, 190, 193, 196, 199, 204, 206
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Corresponding Fibonacci numbers are given by A084910.
|
|
EXAMPLE
|
(sqrt(5)-1)/2 = 1/F(2) + 1/F(6) + 1/F(8) + 1/F(10) + 1/F(17) + 1/F(21) + ...
= 1/2 + 1/13 + 1/34 + 1/89 + 1/2584 + 1/17711 + 1/75025 +...
|
|
PROGRAM
|
(PARI) x=(sqrt(5)-1)/2; a=2; S=0; for(n=1, 100, b=a+1; while(abs(S+1/fibonacci(b))>x, b++); S=S+1/fibonacci(b); a=b; print1(b-1, ", "))
|
|
CROSSREFS
|
Cf. A084907, A084910.
Sequence in context: A141105 A047395 A036554 this_sequence A038619 A118257 A066762
Adjacent sequences: A084906 A084907 A084908 this_sequence A084910 A084911 A084912
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jun 10 2003
|
|
|
Search completed in 0.002 seconds
|
