A382128 Fractalization of the Recamán sequence.

0, 0, 1, 0, 3, 1, 6, 0, 2, 3, 7, 1, 13, 6, 20, 0, 12, 2, 21, 3, 11, 7, 22, 1, 10, 13, 23, 6, 9, 20, 24, 0, 8, 12, 25, 2, 43, 21, 62, 3, 42, 11, 63, 7, 41, 22, 18, 1, 42, 10, 17, 13, 43, 23, 16, 6, 44, 9, 15, 20, 45, 24, 14, 0, 46, 8, 79, 12, 113, 25, 78, 2, 114, 43, 77, 21, 39, 62, 78

Offset: 1

Author

David Cleaver, Mar 16 2025

Keywords

• nonn
• easy

Comments

Self-descriptive sequence: even indexed terms are the sequence itself, odd indexed terms are the Recamán sequence.

This is an r1k1 fractal sequence, where r1k1 means: remove 1 term, keep 1 term, repeat. The Removed terms are the sequence that has been fractalized, and the Kept terms are the original fractal sequence.

This fractal sequence is not a Kimberling fractal sequence because if you delete the first occurrence of each term, the remaining sequence is not the same as the original. This sequence fails to be a Kimberling fractal due to having consecutive terms that both appeared earlier in the sequence, starting with the 1 and 42 at index 48 and 49, respectively.

Links

• David Cleaver, Table of n, a(n) for n = 1..10000
• Clark Kimberling, Fractal sequences.

Crossrefs

Cf. A005132, A003602, A110766, A110779, A110812, A382129, A382130.

Formula

a(2n) = a(n); a(2n-1) = A005132(n), n >= 1.

a(n) = A005132(A003602(n)).