A074778 Numbers k such that 2^k+1 and F(k) are not relatively prime, where F(k) denotes the k-th Fibonacci number.

10, 14, 30, 36, 42, 50, 54, 70, 74, 90, 98, 100, 108, 110, 114, 126, 130, 134, 150, 154, 162, 170, 174, 178, 180, 182, 190, 192, 194, 202, 210, 222, 230, 238, 250, 252, 254, 266, 270, 290, 294, 300, 310, 322, 324, 330, 340, 342, 350, 352, 354, 370, 378, 390

Offset

1,1

Comments

If n is in the sequence, then so is k*n for all odd k. - Robert Israel, Jan 10 2018

Links

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

Formula

a(n) seems to be asymptotic to c*n with c=5.8...

Maple

N:= 100:
R:= NULL:
count:= 0:
for n from 1 while count < N do
  if igcd(2^n+1, combinat:-fibonacci(n)) > 1 then
    count:= count+1;
    R:= R, n
  fi
od:
R; # Robert Israel, Jan 10 2018

Mathematica

Select[Range[400], !CoprimeQ[2^# + 1, Fibonacci[#]] &] (* Amiram Eldar, May 20 2022 *)

Prog

(PARI) isok(n) = gcd(2^n+1, fibonacci(n)) != 1; \\ Michel Marcus, Jan 10 2018

Crossrefs

Cf. A000045, A000051.

Sequence in context: A031028 A176810 A115603 * A162899 A115391 A241162

Adjacent sequences: A074775 A074776 A074777 * A074779 A074780 A074781

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Status

approved