A271750 a(1) = 1; a(n+1) = smallest Fibonacci number > a(n) with leading digit equal to the final digit of a(n).

1, 13, 34, 4181, 10946, 63245986, 6557470319842, 27777890035288, 806515533049393, 3416454622906707, 7540113804746346429, 927372692193078999176, 6356306993006846248183, 3311648143516982017180081, 14028366653498915298923761, 155576970220531065681649693, 30960598847965113057878492344

Offset

1,2

Comments

Look at this array:

...1

...13

....34

.....4181

........10946

............63245986

...................6557470319842

.

.

.

................................34507973060837282187130139035400899082304280

Since no positive Fibonacci number begins with 0, the sequence ends here.

- N. J. A. Sloane, May 02 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..25

Example

Since a(1) = 1, a(2) must start with 1 and so a(2) = 13;
since a(2) = 13, a(3) must start with 3, and so a(3) = 34;
since a(3) = 34, a(4) must start with 4 and the smallest Fibonacci number greater than 34 and beginning with 4 is 4181; ...

Mathematica

F = Fibonacci; L={2}; While[(d = Mod[F[k = Last@L], 10]) > 0, While[ IntegerDigits[ F[++k]][[1]] != d]; AppendTo[L, k]]; F@L (* Giovanni Resta, May 02 2016 *)

Crossrefs

Cf. A061448.

Sequence in context: A214729 A280322 A262851 * A082214 A115161 A063300

Adjacent sequences: A271747 A271748 A271749 * A271751 A271752 A271753

Keyword

nonn,base,fini,full

Author

José de Jesús Camacho Medina, Apr 13 2016

Status

approved