A378243 a(n) is the least k > 0 such that n belongs to a Fibonacci-like sequence starting with initial values A378242(i) and A378242(j) for some i, j <= n.

1, 2, 2, 2, 3, 2, 4, 4, 2, 3, 4, 5, 3, 2, 3, 5, 4, 5, 4, 6, 3, 2, 5, 3, 7, 6, 4, 8, 5, 9, 4, 8, 3, 4, 2, 5, 10, 3, 6, 6, 9, 5, 4, 7, 6, 5, 8, 10, 4, 6, 11, 8, 3, 4, 7, 2, 9, 6, 5, 6, 3, 11, 9, 10, 9, 6, 12, 5, 4, 6, 12, 13, 7, 5, 7, 13, 10, 9, 4, 6, 7, 8, 9, 8

Offset

0,2

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, C++ program

Formula

a(A378242(n)) = n, and this is the first occurrence of n in the sequence.

a(n) = 2 iff n is a positive Fibonacci number.

Example

The first terms, alongside possible values for i and j, are:
  n   a(n)  i  j  A378242(i)  A378242(j)
  --  ----  -  -  ----------  ----------
   0     1  1  1           0           0
   1     2  1  2           0           1
   2     2  1  2           0           1
   3     2  1  2           0           1
   4     3  1  3           0           4
   5     2  1  2           0           1
   6     4  1  4           0           6
   7     4  2  4           1           6
   8     2  1  2           0           1
   9     3  2  3           1           4
  10     4  3  4           4           6

Prog

(C++) // See Links section.

Crossrefs

Cf. A378242.

Sequence in context: A035433 A029199 A121611 * A360106 A300066 A286545

Adjacent sequences: A378240 A378241 A378242 * A378244 A378245 A378246

Keyword

nonn

Author

Rémy Sigrist, Nov 20 2024

Status

approved