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 A378098 #9 Nov 17 2024 07:16:05 %S A378098 2,4,5,10,6,8,9,12,14,16,13,26,18,15,20,22,19,38,24,21,27,30,25,35,28, %T A378098 32,34,36,23,46,33,39,42,40,44,48,41,82,50,45,51,54,47,94,52,56,49,63, %U A378098 57,60,55,65,58,62,64,66,68,70,61,122,72,69,75,78,74,76,71,142,80,84,77,88,79,158,86,90,81,87,93,96,92,98,85,95,100,102,99,105,91,104 %N A378098 Lexicographically earliest sequence of distinct positive integers such that a(a(n)) shares a factor with a(a(n)-1). %C A378098 A self-referencing EKG-type sequence. The terms appear to be concentrated along two lines, a lower straight line where a(n) is slightly above n and an upper straight line where a(n) is approximately 2*n. For larger values of n the later line is composed solely of even semiprimes. %C A378098 In the first 100000 terms there are no fixed points, and it is likely none exist. In the same range there are only two terms where a(n) is less than n, for a(29) = 23 and a(97) = 89. %C A378098 The missing numbers are 1, 3, 7, 11, 17, 29, 31, 37, 43, 53, 59, 67, 73, 83, ... . %H A378098 Scott R. Shannon, <a href="/A378098/b378098.txt">Table of n, a(n) for n = 1..10000</a> %e A378098 a(2) = 4 as a(1) = 2 and 4 is the smallest unused number that shares a factor with a(2-1) = a(1) = 2. %e A378098 a(3) = 5 as a(3) is not referenced earlier in the sequence so it is the lowest unused number that does not violate the sharing factor requirement. It cannot be 3 as that would require a(3) = 3 to share a factor with a(3-1) = a(2) = 4, which is does not, and it cannot be 4 as that has already been used. %Y A378098 Cf. A064413, A378030, A121053, A027746. %K A378098 nonn %O A378098 1,1 %A A378098 _Scott R. Shannon_, Nov 16 2024