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 A381900 #13 May 25 2025 09:22:31 %S A381900 1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,3,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,3,1,1, %T A381900 1,1,2,1,1,1,1,2,4,1,1,1,1,2,3,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,3,1,1,1, %U A381900 1,2,1,1,1,1,2,1,1,1,1,2,3,1,1,1,1,2,4,1,1,1,1,2,1,1,1,1,2,3,1,1,1,1,2,1,1,1,1,2,5 %N A381900 Sequence where k is appended after every (2^(k-1))*k occurrences of 1, with multiple values following a 1 listed in order. %C A381900 The frequencies of the terms follow the logarithmic distribution with parameter value 1/2. %C A381900 The geometric mean approaches A381898 in the limit. %H A381900 Jwalin Bhatt, <a href="/A381900/b381900.txt">Table of n, a(n) for n = 1..10000</a> %H A381900 Wikipedia, <a href="https://en.wikipedia.org/wiki/Logarithmic_distribution">Logarithmic distribution</a> %e A381900 After every (2*2=4) ones we see a 2, %e A381900 after every (4*3=12) ones we see a 3, %e A381900 after every (8*4=32) ones we see a 4 and so on. %o A381900 (Python) %o A381900 from itertools import islice %o A381900 def logarithmic_distribution_generator(): %o A381900 num_ones, num_reached = 0, 1 %o A381900 while num_ones := num_ones+1: %o A381900 yield 1 %o A381900 for num in range(2, num_reached+2): %o A381900 if num_ones % ((2**(num-1))*(num)) == 0: %o A381900 yield num %o A381900 num_reached += num == num_reached+1 %o A381900 A381900 = list(islice(logarithmic_distribution_generator(), 120)) %Y A381900 Cf. A381522, A381898. %K A381900 nonn %O A381900 1,5 %A A381900 _Jwalin Bhatt_, Mar 09 2025