A274243 Numbers n for which the sum of the odd numbers in the Collatz (3x+1) iteration of n is prime.

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,...

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