

A129322


Triangle where the nth row lists the smallest n positive integers which are coprime to the nth 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
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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, m1)+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



