cp's OEIS Frontend

A361314 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number which has not appeared that shares a factor with a(n-2) + a(n-1) while the sum a(n) + a(n-1) is distinct from all previous sums a(i) + a(i-1), i=2..n-1.

%I A361314 #17 Mar 09 2023 06:17:39
%S A361314 1,2,3,5,4,6,8,7,9,10,19,29,12,41,53,14,67,15,16,31,47,13,20,18,22,24,
%T A361314 26,25,17,27,28,11,21,36,30,32,38,34,39,73,35,33,42,45,48,51,44,40,46,
%U A361314 43,89,50,139,49,52,101,54,55,109,56,57,113,58,60,59,63,61,62,66,64,65,69,68,137,70
%N A361314 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number which has not appeared that shares a factor with a(n-2) + a(n-1) while the sum a(n) + a(n-1) is distinct from all previous sums a(i) + a(i-1), i=2..n-1.
%C A361314 In the first 100000 terms the fixed points are 1, 2, 3, 6, 9, 10, 39, 91, 112; it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.
%H A361314 Scott R. Shannon, <a href="/A361314/a361314.png">Image for n = 1..100000</a>. The green line is a(n) = n.
%e A361314 a(23) = 20 as a(21) + a(22) = 47 + 13 = 60, and 20 is the smallest unused number that shares a factor with 60 while the sum a(22) + 20 = 13 + 20 = 33 is distinct from all previous sums. Note that 18 is unused and shares a factor with 60 but the sum a(22) + 18 = 13 + 18 = 31 is the same as a(18) + a(19) = 15 + 16 = 31. This is the first term that differs from A337136.
%Y A361314 Cf. A337136, A359799, A354755, A354727, A354687, A354753, A353989, A354087, A352763.
%K A361314 nonn
%O A361314 1,2
%A A361314 _Scott R. Shannon_, Mar 08 2023