A177231 Fibonacci numbers whose decimal expansion does not contain any digit "2".

0, 1, 3, 5, 8, 13, 34, 55, 89, 144, 377, 610, 987, 1597, 4181, 6765, 10946, 17711, 46368, 196418, 317811, 39088169, 165580141, 433494437, 701408733, 1134903170, 1836311903, 17167680177565, 117669030460994, 806515533049393, 99194853094755497, 160500643816367088

Offset: 1

Author

Carmine Suriano, May 05 2010

Keywords

• nonn
• base

Comments

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".

Examples

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

Crossrefs

Cf. A000045, A177194, A177195, A176253.

Programs

Magma

[0] cat [Fibonacci(n): n in [2..150] | not 2 in Intseq(Fibonacci(n))]; // Vincenzo Librandi, May 09 2019

Maple

F:= combinat[fibonacci]:
q:= n-> not(2 in convert(n, base, 10)):
select(q, {F(n)$n=0..101})[];  # Alois P. Heinz, May 06 2019

Mathematica

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

Extensions

Edited by Charles R Greathouse IV, Aug 03 2010

a(1) changed from 1 to 0 by Alois P. Heinz, May 06 2019