A253676 Irregular triangle T read by rows in which row n is the result of iterating the function S defined in A257480 and terminating at the first occurrence of 1, assuming the 3x+1 (or Collatz) conjecture.

1, 2, 1, 3, 5, 4, 2, 1, 4, 2, 1, 5, 4, 2, 1, 6, 1, 7, 8, 5, 4, 2, 1, 8, 5, 4, 2, 1, 9, 7, 8, 5, 4, 2, 1, 10, 5, 4, 2, 1, 11, 41, 31, 35, 59, 149, 112, 95, 107, 608, 770, 145, 109, 82, 16, 14, 2, 1, 12, 5, 4, 2, 1, 13, 10, 5, 4, 2, 1, 14, 2, 1, 15, 17, 13, 10, 5, 4, 2, 1

Offset: 1

Author

L. Edson Jeffery, May 02 2015

Keywords

• nonn
• tabf

Examples

			T begins:
.    1
.    2  1
.    3  5  4  2  1
.    4  2  1
.    5  4  2  1
.    6  1
.    7  8  5  4  2   1
.    8  5  4  2  1
.    9  7  8  5  4   2   1
.   10  5  4  2  1
.   11 41 31 35 59 149 112 95 107 608 770 145 109 82 16 14 2 1
.   12  5  4  2  1
.   13 10  5  4  2   1
.   14  2  1
.   15 17 13 10  5   4   2  1
		

Crossrefs

Cf. A257480 and cross references therein.

Programs

Mathematica

v[n_] := IntegerExponent[n, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; s[n_] := (3 + (3/2)^v[1 + f[4*n - 3]]*(1 + f[4*n - 3]))/6; t[n_] := NestWhileList[s[#] &, n, # > 1 &]; Flatten[Table[t[n], {n, 15}]] (* Replace Flatten with Grid to get the irregular triangle. *)