A072509 Number of Fibonacci numbers F(k) <= 10^n which end in 1.

2, 2, 3, 3, 4, 5, 6, 6, 6, 7, 7, 7, 8, 10, 11, 11, 11, 13, 13, 14, 14, 15, 15, 15, 15, 17, 18, 19, 19, 20, 21, 22, 22, 22, 23, 23, 23, 23, 26, 27, 27, 27, 29, 29, 30, 30, 31, 31, 31, 31, 32, 34, 35, 35, 36, 37, 38, 38, 38, 39, 39, 39, 39, 42, 42, 43, 43, 45, 45, 46, 46, 47, 47

Offset: 0

Author

Vladeta Jovovic, Aug 23 2002

Keywords

• base
• easy
• nonn

Comments

Note that F(k) ends in 1 if and only if k == 1, 2, 8, 19, 22, 28, 41, or 59 (mod 60). - Robert Israel, May 14 2018

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Different from A073550. Cf. A072353, A072675.

Programs

Maple

N:= 100: m:= 0:
A:= Array(0..N):
A[0]:= 2:
for i from 0 while m <= N do
  for j in [1, 2, 8, 19, 22, 28, 41, 59] do
    m:= ilog10(combinat:-fibonacci(60*i+j))+1;
    if m > N then break fi;
    A[m..N]:= A[m..N]+1;
od od:
convert(A,list); # Robert Israel, May 14 2018

Mathematica

With[{s = Array[Fibonacci, 350]}, Table[Count[TakeWhile[s, # <= 10^n &], ?(Mod[#, 10] == 1 &)], {n, 0, IntegerLength@ Max@ s}] ] (* _Michael De Vlieger, May 14 2018 *)