A177231 - OEIS

%I #22 Sep 08 2022 08:45:53

%S 0,1,3,5,8,13,34,55,89,144,377,610,987,1597,4181,6765,10946,17711,

%T 46368,196418,317811,39088169,165580141,433494437,701408733,

%U 1134903170,1836311903,17167680177565,117669030460994,806515533049393,99194853094755497,160500643816367088

%N Fibonacci numbers whose decimal expansion does not contain any digit "2".

%C The probability that Fibonacci(n) contains no 2's goes to zero as n grows to infinity. The maximum term is possibly Fibonacci(101) having 21 digits, none of them being "2".

%e a(5) = 8 is the 5th Fibonacci number having no digit 2's.

%p F:= combinat[fibonacci]:

%p q:= n-> not(2 in convert(n, base, 10)):

%p select(q, {F(n)$n=0..101})[];  # _Alois P. Heinz_, May 06 2019

%t Join[{0}, Select[Fibonacci[Range[2, 50]], DigitCount[#, 10, 2]==0&]] (* _Harvey P. Dale_, Oct 01 2017 *)

%o (Magma) [0] cat [Fibonacci(n): n in [2..150] | not 2 in Intseq(Fibonacci(n))]; // _Vincenzo Librandi_, May 09 2019

%Y Cf. A000045, A177194, A177195, A176253.

%K nonn,base

%O 1,3

%A _Carmine Suriano_, May 05 2010

%E Edited by _Charles R Greathouse IV_, Aug 03 2010

%E a(1) changed from 1 to 0 by _Alois P. Heinz_, May 06 2019