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

1,1

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.

Formula

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A256267 A307687 A281121 * A378744 A394188 A220949

Adjacent sequences: A382126 A382127 A382128 * A382130 A382131 A382132

Keyword

nonn,easy

Author

David Cleaver, Mar 16 2025

Status

approved