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 A378297 #21 Dec 23 2024 02:16:59
%S A378297 38,46,106,129,133,201,235,334,335,381,417,458,489,538,579,583,597,
%T A378297 623,626,685,689,694,767,781,898,921,1073,1082,1099,1214,1226,1227,
%U A378297 1234,1285,1299,1315,1385,1486,1514,1517,1546,1603,1631,1646,1799,1817,1819,1841
%N A378297 Squarefree semiprimes k that remain squarefree semiprimes for exactly two iterations of the map k -> 2*k+1.
%e A378297 38 is a term because 38 (semiprime) gives 2*38+1 (77, semiprime) gives 2*77+1 (155, semiprime). But 155 gives 2*155+1 (311, not semiprime), so the chain has length three (38, 77, 155).
%e A378297 921 is a term because 921 (semiprime) gives 2*921+1 (1843, semiprime) gives 2*1843+1 (3687, semiprime). But 3687 gives 2*3687+1 (7375, not semiprime), so the chain has length three (921, 1843, 3687).
%t A378297 s[n_] := -1 + Length@ NestWhileList[2*# + 1 &, n, FactorInteger[#][[;; , 2]] == {1, 1} &]; Select[Range[2000], s[#] == 3 &] (* _Amiram Eldar_, Dec 17 2024 *)
%Y A378297 Cf. A177221, A006881.
%K A378297 nonn,easy
%O A378297 1,1
%A A378297 _Paul Duckett_, Nov 22 2024