A129322 Triangle where the n-th row lists the smallest n positive integers which are coprime to the n-th Fibonacci number.

1, 1, 2, 1, 3, 5, 1, 2, 4, 5, 1, 2, 3, 4, 6, 1, 3, 5, 7, 9, 11, 1, 2, 3, 4, 5, 6, 7, 1, 2, 4, 5, 8, 10, 11, 13, 1, 3, 5, 7, 9, 11, 13, 15, 19, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 26

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, flattened).

Example

The 8th Fibonacci number is 21. So row 8 lists the 8 smallest positive integers which are coprime to 21: (1,2,4,5,8,10,11,13).
1;
1,2;
1,3,5;
1,2,4,5;
1,2,3,4,6;
1,3,5,7,9,11;
1,2,3,4,5,6,7;
1,2,4,5,8,10,11,13;
1,3,5,7,9,11,13,15,19;
1,2,3,4,6,7,8,9,12,13;

Maple

A129322 := proc(n, m)
    option remember;
    local f, a;
    f := combinat[fibonacci](n) ;
    if m = 1 then
        return 1;
    else
        for a from procname(n, m-1)+1 do
            if igcd(f, a) = 1 then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Dec 14 2016

Mathematica

Table[Block[{m = Fibonacci@n, r = {1}, k = 2}, While[Length@ r < n, If[GCD[k, m] == 1, AppendTo[r, k], Nothing]; k++]; r], {n, 16}] // Flatten (* Michael De Vlieger, Dec 26 2019 *)

Crossrefs

Cf. A120839 (diagonal).

Sequence in context: A085189 A130466 A239306 * A089984 A284429 A062105

Adjacent sequences: A129319 A129320 A129321 * A129323 A129324 A129325

Keyword

nonn,tabl

Author

Leroy Quet, May 26 2007

Extensions

More terms from R. J. Mathar, Nov 01 2007

Status

approved