A382128 -id:A382128 - cp's OEIS frontend

A382130 Fractalization of the golden ratio.

1, 1, 6, 1, 1, 6, 8, 1, 0, 1, 3, 6, 3, 8, 9, 1, 8, 0, 8, 1, 7, 3, 4, 6, 9, 3, 8, 8, 9, 9, 4, 1, 8, 8, 4, 0, 8, 8, 2, 1, 0, 7, 4, 3, 5, 4, 8, 6, 6, 9, 8, 3, 3, 8, 4, 8, 3, 9, 6, 9, 5, 4, 6, 1, 3, 8, 8, 8, 1, 4, 1, 0, 7, 8, 7, 8, 2, 2, 0, 1, 3, 0, 0, 7, 9, 4, 1, 3, 7, 5, 9, 4, 8, 8, 0

Offset: 1

David Cleaver, Mar 16 2025

Self-descriptive sequence: even indexed terms are the sequence itself, odd indexed terms are the decimal digits of the golden ratio.
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.

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

Bisection gives A001622 (odd part).

Cf. A003602, A110766, A110779, A110812, A382128, A382129.

a(2n) = a(n); a(2n-1) = A001622(n), n >= 1.

a(n) = A001622(A003602(n)).

A382129 Fractalization of the prime numbers.

Original entry on oeis.org

2, 2, 3, 2, 5, 3, 7, 2, 11, 5, 13, 3, 17, 7, 19, 2, 23, 11, 29, 5, 31, 13, 37, 3, 41, 17, 43, 7, 47, 19, 53, 2, 59, 23, 61, 11, 67, 29, 71, 5, 73, 31, 79, 13, 83, 37, 89, 3, 97, 41, 101, 17, 103, 43, 107, 7, 109, 47, 113, 19, 127, 53, 131, 2, 137, 59, 139, 23, 149, 61, 151, 11, 157

Offset: 1

David Cleaver, Mar 16 2025

Self-descriptive sequence: even indexed terms are the sequence itself, odd indexed terms are the prime numbers.
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 also a Kimberling fractal sequence because if you delete the first occurrence of each term, the remaining sequence is the same as the original.

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

Cf. A000040, A003602, A110766, A110779, A110812, A382128, A382130.

a[n_] := Prime[(n/2^IntegerExponent[n, 2] + 1)/2]; Array[a, 100] (* Amiram Eldar, Mar 21 2025 *)

a(2n) = a(n); a(2n-1) = A000040(n), n >= 1.

a(n) = A000040(A003602(n)).

cp's OEIS Frontend

A382130 Fractalization of the golden ratio.

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