Odd numbers whose Collatz trajectory contains exactly 12 odd numbers.

0

`%I #21 Jul 18 2022 19:07:25
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`%S 39,79,153,157,305,307,315,317,611,613,629,631,647,683,687,1221,1229,
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`%T 1241,1257,1261,1265,1269,1295,1353,1367,1369,1375,1505,2445,2453,
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`%U 2481,2483,2489,2507,2515,2517,2521,2525,2531,2545,2589,2593,2633,2705,2707,2733
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`%N Odd numbers whose Collatz trajectory contains exactly 12 odd numbers.
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`%F { A005408 } intersect { A072122 }.
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`%e 305 is a term since its Collatz trajectory is 305, 916, 458, 229, 688, 344, 172, 86, 43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
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`%t q[n_] := Count[NestWhileList[If[OddQ[#], 3 # + 1, #/2] &, n, # > 1 &], _?OddQ] == 12; Select[Range[1, 2750, 2], q] (* _Amiram Eldar_, May 20 2022 *)
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`%Y Cf. A005408, A072122.
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`%K nonn
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`%O 1,1
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`%A _Krishna Kumar Arumugam_, May 20 2022
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