A121730 a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to the n-th Fibonacci number.

1, 2, 3, 4, 6, 5, 7, 8, 9, 12, 10, 11, 13, 14, 17, 16, 15, 21, 18, 19, 23, 20, 22, 25, 24, 26, 27, 28, 29, 37, 30, 31, 33, 32, 34, 35, 36, 38, 39, 43, 40, 41, 42, 44, 47, 45, 46, 53, 48, 49, 51, 50, 52, 55, 54, 59, 57, 56, 58, 67, 60, 61, 63, 62, 64, 65, 66, 68, 69, 72, 70, 71

Offset

1,2

Comments

Sequence is a permutation of the positive integers.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

55 is the 10th Fibonacci number. Among those positive integers not occurring among the first 9 terms of the sequence, 12 is the smallest which is coprime to 55, so a(10) = 12. 10 and 11 also do not occur among the first 9 terms of the sequence, but they are not coprime to 55.

Maple

L:= [$1..100]: # for all terms before the first term > 100
for n from 1 do
  v:= combinat:-fibonacci(n);
  found:= false;
  for j from 1 to nops(L) do
    if igcd(L[j], v)=1 then
      A[n]:= L[j];
      L:= subsop(j=NULL, L);
      found:= true;
      break
    fi;
  od;
  if not found then break fi
od:
seq(A[i], i=1..n-1); # Robert Israel, Jun 26 2018

Crossrefs

Cf. A000045, A121731.

Sequence in context: A130946 A073284 A057511 * A275659 A244321 A364824

Adjacent sequences: A121727 A121728 A121729 * A121731 A121732 A121733

Keyword

nonn

Author

Leroy Quet, Aug 18 2006

Extensions

Extended by Ray Chandler, Aug 22 2006

Status

approved