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Numbers n for which the sum of the numbers in the Collatz (3x+1) iteration of n is prime.
2

%I #5 May 14 2013 13:56:42

%S 2,4,12,16,22,38,48,52,64,66,67,90,93,132,148,149,155,163,165,185,201,

%T 208,222,229,230,237,242,264,268,275,289,309,324,332,339,351,352,359,

%U 362,363,373,382,384,401,403,465,471,474,485,507,517,518,528,532

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

%e 12 is a member since 12 + 6 + 3 + 10 + 5 + 16 + 8 + 4 + 2 + 1 = 67 is a prime.

%t coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1] &,n,#>1 &]; Select[Range[500],PrimeQ[Total[coll[#]]] &]

%Y Cf. A033493.

%K nonn

%O 1,1

%A _Jayanta Basu_, May 14 2013