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 A274243 Numbers n for which the sum of the odd numbers in the Collatz (3x+1) iteration of n is prime. 0
 11, 13, 22, 26, 44, 52, 53, 67, 88, 104, 105, 106, 113, 121, 131, 134, 165, 176, 187, 208, 210, 211, 212, 226, 227, 231, 242, 243, 257, 261, 262, 268, 273, 289, 291, 293, 325, 329, 330, 352, 373, 374, 416, 419, 420, 422, 424, 431, 447, 452, 454, 461, 462, 473 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding primes are 47, 19, 47, 19, 47, 19, 59, 263, 47, 19, 947, 59, 199, 19777, 419, 263, 20359, 47, 1759, 19, 947, 1291, 59, 199, 569, 23813, 19777, 20173,... LINKS Table of n, a(n) for n=1..54. EXAMPLE 11 is in the sequence because the Collatz trajectory of 11 is 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 and the sum of the odd terms is 11 + 17 + 13 + 5 + 1 = 47 is prime. MATHEMATICA lst={}; coll[n_]:=NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; a:=Select[coll[n], OddQ[#]&]; Do[s=Sum[a[[i]], {i, 1, Length[a]}]; If[PrimeQ[s], AppendTo[lst, n]], {n, 1, 500}]; lst CROSSREFS Cf. A033493, A225748. Sequence in context: A257864 A248599 A366379 * A192931 A002367 A160373 Adjacent sequences: A274240 A274241 A274242 * A274244 A274245 A274246 KEYWORD nonn AUTHOR Michel Lagneau, Jul 01 2016 STATUS approved

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)