A378297 Squarefree semiprimes k that remain squarefree semiprimes for exactly two iterations of the map k -> 2*k+1.

38, 46, 106, 129, 133, 201, 235, 334, 335, 381, 417, 458, 489, 538, 579, 583, 597, 623, 626, 685, 689, 694, 767, 781, 898, 921, 1073, 1082, 1099, 1214, 1226, 1227, 1234, 1285, 1299, 1315, 1385, 1486, 1514, 1517, 1546, 1603, 1631, 1646, 1799, 1817, 1819, 1841

Offset: 1

Author

Paul Duckett, Nov 22 2024

Keywords

• nonn
• easy

Examples

			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).
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).
		

Crossrefs

Cf. A177221, A006881.

Programs

Mathematica

s[n_] := -1 + Length@ NestWhileList[2*# + 1 &, n, FactorInteger[#][[;; , 2]] == {1, 1} &]; Select[Range[2000], s[#] == 3 &] (* Amiram Eldar, Dec 17 2024 *)