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A348136 Irregular triangle read by rows T(n,k) in which row n lists the first digit of every term of the trajectory of n in Collatz problem including the trajectory [1, 4, 2, 1] for n = 1.

%I A348136 #31 Oct 29 2021 09:09:06
%S A348136 1,4,2,1,2,1,3,1,5,1,8,4,2,1,4,2,1,5,1,8,4,2,1,6,3,1,5,1,8,4,2,1,7,2,
%T A348136 1,3,1,5,2,1,4,2,1,5,1,8,4,2,1,8,4,2,1,9,2,1,7,2,1,3,1,5,2,1,4,2,1,5,
%U A348136 1,8,4,2,1,1,5,1,8,4,2,1,1,3,1,5,2,1,4,2,1,5,1,8,4,2,1,1,6,3,1,5,1,8,4,2,1
%N A348136 Irregular triangle read by rows T(n,k) in which row n lists the first digit of every term of the trajectory of n in Collatz problem including the trajectory [1, 4, 2, 1] for n = 1.
%H A348136 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A348136 <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>
%F A348136 a(m) = A000030(A235795(m)), m >= 1.
%F A348136 T(n,k) = A000030(A235795(n,k)).
%e A348136 Triangle begins:
%e A348136 1,4,2,1;
%e A348136 2,1;
%e A348136 3,1,5,1,8,4,2,1;
%e A348136 4,2,1;
%e A348136 5,1,8,4,2,1;
%e A348136 6,3,1,5,1,8,4,2,1;
%e A348136 7,2,1,3,1,5,2,1,4,2,1,5,1,8,4,2,1;
%e A348136 8,4,2,1;
%e A348136 9,2,1,7,2,1,3,1,5,2,1,4,2,1,5,1,8,4,2,1;
%e A348136 1,5,1,8,4,2,1;
%e A348136 1,3,1,5,2,1,4,2,1,5,1,8,4,2,1;
%e A348136 1,6,3,1,5,1,8,4,2,1;
%e A348136 1,4,2,1,5,1,8,4,2,1;
%e A348136 1,7,2,1,3,1,5,2,1,4,2,1,5,1,8,4,2,1;
%e A348136 ...
%t A348136 Prepend[Map[First@ IntegerDigits[#] &, Array[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, #, # > 1 &] &, 11, 2], {2}], NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, 1, # > 1 &, {2, 1}]] // Flatten (* _Michael De Vlieger_, Oct 27 2021 *)
%Y A348136 First digit of every term of A235795.
%Y A348136 First column gives A000030.
%Y A348136 Cf. A006370, A014682, A070165, A235800, A347270 (all 3x+1 sequences).
%K A348136 nonn,base,tabf
%O A348136 1,2
%A A348136 _Omar E. Pol_, Oct 02 2021