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A129322 Triangle where the n-th row lists the smallest n positive integers which are coprime to the n-th Fibonacci number. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)