This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382129 #29 Mar 22 2025 22:50:51 %S A382129 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, %T A382129 47,19,53,2,59,23,61,11,67,29,71,5,73,31,79,13,83,37,89,3,97,41,101, %U A382129 17,103,43,107,7,109,47,113,19,127,53,131,2,137,59,139,23,149,61,151,11,157 %N A382129 Fractalization of the prime numbers. %C A382129 Self-descriptive sequence: even indexed terms are the sequence itself, odd indexed terms are the prime numbers. %C A382129 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. %C A382129 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. %H A382129 David Cleaver, <a href="/A382129/b382129.txt">Table of n, a(n) for n = 1..10000</a> %H A382129 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">Fractal sequences</a>. %F A382129 a(2n) = a(n); a(2n-1) = A000040(n), n >= 1. %F A382129 a(n) = A000040(A003602(n)). %t A382129 a[n_] := Prime[(n/2^IntegerExponent[n, 2] + 1)/2]; Array[a, 100] (* _Amiram Eldar_, Mar 21 2025 *) %Y A382129 Cf. A000040, A003602, A110766, A110779, A110812, A382128, A382130. %K A382129 nonn,easy %O A382129 1,1 %A A382129 _David Cleaver_, Mar 16 2025