A382129 Fractalization of the prime numbers.

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

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 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.

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

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