%I #24 May 17 2016 11:18:45
%S 0,1,1,2,3,5,8,13,34,55,89,144,233,377
%N Fibonacci numbers with digits in nondecreasing order.
%C Intersection of A000045 and A009994. - _Felix Fröhlich_, May 16 2016
%C Conjecture: The sequence is finite, with 377 being the last term. I have verified the conjecture up to A000045(10^5). - _Felix Fröhlich_, May 16 2016
%C Conjecture verified up to Fibonacci(10^8). - _Charles R Greathouse IV_, May 17 2016
%t Select[Fibonacci@ Range[0, 10^4], Sort@ # == # &@ IntegerDigits@ # &] (* _Michael De Vlieger_, May 13 2016 *)
%o (PARI) is_a009994(n) = digits(n)==vecsort(digits(n))
%o for(n=0, 1e4, if(is_a009994(fibonacci(n)), print1(fibonacci(n), ", "))) \\ _Felix Fröhlich_, May 16 2016
%o (PARI) fibmod(n,m)=lift(((Mod([1,1;1,0],m))^n)[1,2])
%o isA009994(n)=my(d=digits(n)); vecsort(d)==d
%o B1=10^9;B2=10^57;
%o for(n=1,1e9, if(isA009994(fibmod(n,B1)) && isA009994(fibmod(n,B2)) && isA009994(F=fibonacci(n)), print1(F", "))) \\ _Charles R Greathouse IV_, May 17 2016
%Y Cf. A000045, A009994, A272918, A273046.
%K nonn,base
%O 1,4
%A _Omar E. Pol_, May 13 2016
%E Offset adjusted by _Felix Fröhlich_, May 16 2016