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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
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,...
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
Sequence in context: A257864 A248599 A366379 * A192931 A002367 A160373
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 01 2016
STATUS
approved