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Prime numbers having no additional odd primes in their Collatz (3x+1) trajectory.
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%I #3 Feb 14 2013 20:59:07

%S 2,5,113,227,2417,3637,7253,14549,14563,30559,38677,38833,155333,

%T 206923,207121,217309,464213,466033,620771,827693,915737,1100149,

%U 1100353,1220983,1303873,1472893,1656901,1963813,2327483,2475797,2933717,2933731,3313777,3491083

%N Prime numbers having no additional odd primes in their Collatz (3x+1) trajectory.

%C Sequence A221475 contains odd composite numbers with this property.

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; n = 0; While[Length[t] < 50, n++; p = Prime[n]; If[Union[Drop[PrimeQ[Rest[Collatz[p]]], -2]] == {False}, AppendTo[t, p]]]; t

%Y Cf. A221475.

%K nonn

%O 1,1

%A _T. D. Noe_, Feb 14 2013