|
| |
|
|
A105509
|
|
Numbers n such that 9 is the leading digit of the n-th Fibonacci number in decimal representation.
|
|
9
| |
|
|
16, 35, 59, 83, 102, 126, 150, 169, 193, 212, 236, 260, 279, 303, 327, 346, 370, 394, 413, 437, 461, 480, 504, 528, 547, 571, 595, 614, 638, 657, 681, 705, 724, 748, 772, 791, 815, 839, 858, 882, 906, 925, 949, 973, 992, 1016, 1040, 1059, 1083, 1102, 1107
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| A008963(a(n)) = 9; A105519(a(n)) = A105519(a(n) - 1) + 1.
Comment from Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 23 2006: Peterson says: "Calculate 100/89 = 1.1235955056... This fraction generates the first five Fibonacci numbers before blurring into other digits. ... 10000/9899 = 1.0102030508132134559046368... generates the first 10 Fibonacci numbers (using two digits per number). 1000000/998999 generates the first 15 Fibonacci numbers (using three digits per number). ... in successive fractions, two 0s are appended to the numerator and a 9 to the beginning and end of the denominator...."
|
|
|
REFERENCES
| Bicknell-Johnson, M. 2004. A generalized magic trick from Fibonacci: Designer decimals. College Mathematics Journal 35(March):125-126.
Chan, O-Y. and J. Smoak. 2006. More designer decimals: The integers and their geometric extensions. College Mathematics Journal 37(November):355-363.
|
|
|
LINKS
| Smoak, J. and T.J. Osler, A magic trick from Fibonacci. College Mathematics Journal, 34 (2003):58-60.
Ivars Peterson, Designer Decimals, Science News, Week of Nov. 4, 2006; Vol. 170, No. 19.
|
|
|
FORMULA
| n such that d(n+5)-d(n) = 2 for d(n) = floor(1 + log base 10(F(n))) and F(n) = n-th Fibonacci number = A000045(n). - Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 23 2006
|
|
|
EXAMPLE
| a(10)=21: A008963(212) = A000030(A000045(212)) =
A000030(90343046356137747723758225621187571439538669) = 9.
|
|
|
CROSSREFS
| Cf. A000030, A000045, A072711, A105501, A105502, A105503, A105504, A105505, A105506, A105507, A105508.
Sequence in context: A161441 A190741 A086119 * A070588 A183196 A109287
Adjacent sequences: A105506 A105507 A105508 * A105510 A105511 A105512
|
|
|
KEYWORD
| nonn,base
|
|
|
AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 11 2005
|
| |
|
|
