A377536 Integers that are the arithmetic mean of two distinct Fibonacci numbers (A000045).

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 17, 18, 21, 28, 29, 30, 34, 38, 45, 46, 47, 51, 55, 72, 73, 76, 89, 117, 118, 119, 123, 127, 144, 161, 189, 190, 191, 195, 199, 216, 233, 305, 306, 309, 322, 377, 494, 495, 496, 500, 504, 521, 538, 610, 682, 799, 800, 801, 805

Offset

1,2

Comments

This sequence contains all positive Fibonacci numbers of A000045. Proof: For i >= 2, (F(i-2) + F(i+1))/2 = (F(i-2) + F(i-1) + F(i))/2 = (F(i-2) + F(i-1) + F(i-2) + F(i-1))/2 = F(i-1) + F(i-2) = F(i).

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Fibonacci Number

Example

1 is in the sequence because (F(0) + F(3))/2 = (0 + 2)/2 = 1.
12 is in the sequence because (F(4) + F(8))/2 = (3 + 21)/2 = 12.

Maple

with(combinat):
A377536:=proc(k)
   local L, M, i, j;
   M:={};
   L:=[seq(fibonacci(i), i=0..k)];
   for i to k do
      for j from i+1 to k+1 do
         if is(L[i]+L[j], even) then
            M:=[op(M), (L[i]+L[j])/2]
         fi
      od
   od;
   M:=convert(M, set);
   return op(M)
end proc:
A377536(17)

Crossrefs

Cf. A000045, A084176.

Sequence in context: A353833 A219301 A326155 * A079734 A050730 A288221

Adjacent sequences: A377533 A377534 A377535 * A377537 A377538 A377539

Keyword

nonn

Author

Felix Huber, Dec 18 2024

Status

approved