A291179 Numbers in at least one Fibonacci sequence starting with two 1-digit numbers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110

Offset

1,3

Comments

The first missing positive integer is 106.

Links

Bobby Jacobs, Table of n, a(n) for n = 1..500

Example

100 is in this sequence because 100 is in the Fibonacci sequence starting with 6 and 4: 6, 4, 10, 14, 24, 38, 62, 100, ...

Mathematica

With[{nn = 110}, TakeWhile[Union@ Flatten@ Map[LinearRecurrence[{1, 1}, #, 1 + Floor[1/2 + Log[GoldenRatio, Sqrt[5] nn]]] &, Tuples[Range@ 9, 2]], # <= nn &]] (* Michael De Vlieger, Aug 19 2017 *)
Take[Flatten[LinearRecurrence[{1, 1}, #, 20]&/@Tuples[Range[0, 9], 2]]//Union, 120] (* Harvey P. Dale, Oct 06 2017 *)

Prog

(PARI) list(lim)=if(lim<106, return([0..lim\1])); my(v=List([0..105])); for(t=1, 9, my(x=t, y=t); while(y<=lim, listput(v, y); [x, y]=[y, x+y])); for(m=1, 9, for(n=1, 9, my(x=m, y=n); while(y<=lim, listput(v, y); [x, y]=[y, x+y]))); Set(v) \\ Charles R Greathouse IV, Aug 21 2017

Crossrefs

Cf. A000045, A290948.

Complement of A277605.

Sequence in context: A317945 A292579 A262530 * A033619 A130734 A118759

Adjacent sequences: A291176 A291177 A291178 * A291180 A291181 A291182

Keyword

base,nonn

Author

Bobby Jacobs, Aug 19 2017

Status

approved