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 A351001 #16 Jun 27 2025 08:34:23
%S A351001 0,1,2,6,4,5,3,10,26,8,12,14,13,9,11,15,16,62,18,20,19,21,22,86,24,25,
%T A351001 7,28,30,29,118,27,35,31,32,33,39,34,146,36,38,37,40,42,41,166,23,45,
%U A351001 17,44,122,46,48,47,50,194,52,51,206,514,54,56,55,57,49,53,58,60,59,63,61,64
%N A351001 a(0) = 0, a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared which has a common factor with a(n-2) + a(n-1) but does not equal a(n-2) + a(n-1).
%C A351001 This is a permutation of the natural numbers. Up to 500000 terms the fixed points are 0, 1, 2, 4, 5, 15, 16, 18, 21, 22, 24, 25, 29, and it is likely no more exist.
%H A351001 Scott R. Shannon, <a href="/A351001/a351001.png">Image of the first 500000 terms</a>. The green line is y = n.
%e A351001 a(3) = 6 as a(1)+a(2) = 3, 6 does not equal 3, and gcd(3,6) > 1.
%e A351001 a(4) = 4 as a(2)+a(3) = 8, 4 does not equal 8, and gcd(8,4) > 1.
%t A351001 s = {0, 1, 2}; u = 3; c[_] = 0; Set[{i, j}, s[[-2 ;; -1]]]; Array[Set[c[s[[#]]], #] &, Length[s]]; s~Join~Reap[Do[Set[k, u]; While[Nand[c[k] == 0, GCD[i + j, k] > 1, i + j != k], k++]; Sow[k]; Set[c[k], n]; If[k == u, While[c[u] == 1, u++]]; i = j; j = k, {n, Length[s] + 1, 2^10}]][[-1, -1]] (* _Michael De Vlieger_, Jan 28 2022 *)
%Y A351001 Cf. A337136, A064413, A336957, A098550, A089088, A251622.
%K A351001 nonn
%O A351001 0,3
%A A351001 _Scott R. Shannon_, Jan 28 2022