%I #6 Sep 03 2022 18:08:35
%S 1,3,5,11,17,71,579,2705
%N Records in A355899.
%t nn = 2^16; j = k = r = 1; {1}~Join~Reap[Do[m = # + (j + k)/# &@ GCD[j, k]; If[# > r, r = #; Sow[r]] &[GCD[k, m]]; j = k; k = m, {n, 3, nn}]][[-1, -1]] (* _Michael De Vlieger_, Sep 03 2022 *)
%Y Cf. A351871, A355898, A355899, A355900.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Sep 03 2022
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