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.

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, 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, 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

Offset: 1

Author

Omar E. Pol, Oct 02 2021

Keywords

• nonn
• base
• tabf

Examples

			Triangle begins:
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;
7,2,1,3,1,5,2,1,4,2,1,5,1,8,4,2,1;
8,4,2,1;
9,2,1,7,2,1,3,1,5,2,1,4,2,1,5,1,8,4,2,1;
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;
1,4,2,1,5,1,8,4,2,1;
1,7,2,1,3,1,5,2,1,4,2,1,5,1,8,4,2,1;
...
		

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for sequences related to Benford's law

Crossrefs

First digit of every term of A235795.

First column gives A000030.

Cf. A006370, A014682, A070165, A235800, A347270 (all 3x+1 sequences).

Programs

Mathematica

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 *)

Formula

a(m) = A000030(A235795(m)), m >= 1.

T(n,k) = A000030(A235795(n,k)).