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 A367741 #19 Jan 18 2024 04:41:15 %S A367741 1,3,2,15,4,5,6,35,8,7,10,77,12,11,14,33,16,55,18,143,20,13,22,65,24, %T A367741 25,26,85,28,17,21,187,56,99,32,121,30,253,34,23,36,115,38,45,19,39, %U A367741 76,91,40,49,44,63,46,119,48,221,50,51,52,289,42,323,58,57,29,95,87,133,116,171,62,209,31 %N A367741 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n>3, a(n) has a common factor with a(n-2) but not with a(n-1) or n. %C A367741 This is a variation of the Yellowstone permutation A098550 with an additional restriction that no term a(n) can have a common factor with n. For the sequence to be infinite a(n) must always have a prime factor that is not a factor of n+2. See the examples below. %C A367741 As no term a(3*k), k>=1, can contain 3 as a factor, no term a(3*k+2) can be a power of 3 as it must share a factor with a(3*k). Likewise as a(3*(k+1)) must share a factor with a(3*k+1), the later cannot be a power of 3. Therefore no term, other than a(1), can be a power of 3, although it is likely all other positive numbers appear in the sequence. %C A367741 For the terms studied, other than the first three terms and a(40) = 23 and a(45) = 19, the primes appear in their natural order. %H A367741 Scott R. Shannon, <a href="/A367741/b367741.txt">Table of n, a(n) for n = 1..10000</a> %H A367741 Scott R. Shannon, <a href="/A367741/a367741.png">Image of the first 100000 terms</a>. The green line is a(n) = n. %e A367741 a(4) = 15 as a(2) = 3 which 15 shares a factor with, a(3) = 2 which 15 does not share a factor with, and 15 does not share a factor with n = 4. Also 15 has a prime factor (5) which is not a factor of 4+2 = 6. The later restriction eliminates 9 as a candidate for a(4). %Y A367741 Cf. A368231, A098550, A336957, A064413, A027748. %K A367741 nonn %O A367741 1,2 %A A367741 _Scott R. Shannon_, Nov 29 2023