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 A369652 #14 Jul 22 2025 16:13:30 %S A369652 4,4,6,2,6,11,8,7,11,11,8,10,15,15,12,18,17,30,28,22,21,37,28,38,42, %T A369652 33,22,52,43,56,47,49,57,60,55,54,58,70,52,66,68,57,63,86,58,88,92,66, %U A369652 78,95,85,52,102,70,111,57,117,99,136,104,129,110,146,127,135,132,131,129,126,145,112,150,128,129,154,161,145 %N A369652 Maximal digit in the primorial base representation of the n-th arithmetic derivative of 128. %C A369652 This sequence relates to the question whether A327969(128) has a positive integer value, or whether it is -1 by the escape clause. %C A369652 Note that when iterating the map k -> k' from A276086(A369638(4)) = A276086(15232) = 3299611946113357875 onward, the maximal exponent in the prime factorization (A051903) keeps on decreasing until it reaches 1 at the fifth iteration, and then stays as 1 for three more iterations (with k then 38863666759992439 = 643*60441161368573), but then, alas, on the next iteration, k' = 60441161369216 = 2^7 * 472196573197. %H A369652 Sean A. Irvine, <a href="/A369652/b369652.txt">Table of n, a(n) for n = 0..142</a> %H A369652 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a> %F A369652 a(n) = A328114(A369638(n)). %e A369652 The third arithmetic derivative (A099306) of 128 is 5056, which in primorial base (A049345) is written as 220220, therefore a(3) = 2. %e A369652 The fourth arithmetic derivative (A258644) of 128 is 15232, which in primorial base is written as 663320, therefore a(4) = 6. %Y A369652 Cf. A003415, A049345, A099306, A258644, A328114, A369638. %Y A369652 Cf. also A327969. %K A369652 nonn %O A369652 0,1 %A A369652 _Antti Karttunen_, Feb 04 2024