A068498 Fibonacci numbers whose sum of decimal digits is greater than its index.

8, 89, 377, 987, 1597, 2584, 6765, 28657, 46368, 196418, 3524578, 5702887, 39088169, 63245986, 267914296, 4807526976, 7778742049, 139583862445, 591286729879, 17167680177565, 27777890035288, 1304969544928657, 5527939700884757, 8944394323791464

Offset

1,1

Comments

4.5 log(phi)/log(10) = 0.94... < 1, so this sequence is probably finite. The last term appears to be a(224) = F_5832 = 2927...6784; if there is another term it is greater than 10^20000. - Charles R Greathouse IV, Nov 19 2010

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..224

Example

F(11)=89 and 8+9=17 > 11, so 89 is the term of this sequence.

Mathematica

Fibonacci[#]&/@Select[Range[100], Total[IntegerDigits[Fibonacci[#]]]>#&] (* Harvey P. Dale, Apr 14 2014 *)

Prog

(Haskell)
a068498 n = a068498_list !! (n-1)
a068498_list = f [0..] a000045_list where
   f (u:us) (v:vs) = if u < a007953 v then v : f us vs else f us vs
-- Reinhard Zumkeller, Apr 15 2014, Dec 16 2013
(PARI) lista(nn) = {for(n=1, nn, if (sumdigits(f=fibonacci(n)) > n, print1(f, ", "))); } \\ Michel Marcus, Apr 15 2014

Crossrefs

Cf. A000045, A007953.

Sequence in context: A107677 A084005 A137494 * A061000 A240457 A319842

Adjacent sequences: A068495 A068496 A068497 * A068499 A068500 A068501

Keyword

nice,nonn,base

Author

Shyam Sunder Gupta, Mar 25 2002

Extensions

Corrected and extended by Harvey P. Dale, Apr 14 2014

Haskell program and b-file corrected. Thanks to Harvey P. Dale. - Reinhard Zumkeller, Apr 15 2014

Status

approved