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%I #16 Sep 27 2024 20:56:58
%S 12,28,36,44,60,76,92,108,120,124,140,156,164,172,188,204,216,220,236,
%T 248,252,268,284,292,300,316,328,332,348,364,376,380,388,396,412,420,
%U 428,432,436,440,444,460,476,484,492,496,500,504,508,516,524,540,548
%N Numbers that are divisible by 4, but cannot be the largest peak value in a 3x+1 trajectory, regardless of the initial value.
%C It is provable that (beyond 1 and 2) the largest peak value in any 3x+1 (Collatz) trajectory must be a multiple of 4. However, an infinite number of multiples of 4 exist that cannot be the largest peak value of such a trajectory. E.g., no integer of the form 16k+12 = 4*(4k+3) (where k is a nonnegative integer) can be a largest peak value, because the trajectory immediately after the value 16k+12 would consist of the values 8k+6, 4k+3, 12k+10, 6k+5, and 18k+16, which exceeds 16k+12.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%Y Cf. A025586.
%K nonn
%O 1,1
%A _Labos Elemer_, Sep 08 2003
%E Definition and example reworded by _Jon E. Schoenfield_, Sep 01 2013