A381965 Irregular triangle read by rows, where row n lists the iterates of f(x), starting at x = n until f(x) < 10, where f(x) is the multiplicative digital root of x (A031347).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 11, 1, 12, 2, 13, 3, 14, 4, 15, 5, 16, 6, 17, 7, 18, 8, 19, 9, 20, 0, 21, 2, 22, 4, 23, 6, 24, 8, 25, 10, 0, 26, 12, 2, 27, 14, 4, 28, 16, 6, 29, 18, 8, 30, 0, 31, 3, 32, 6, 33, 9, 34, 12, 2, 35, 15, 5, 36, 18, 8, 37, 21, 2

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..11256 (rows 0..3500 of triangle, flattened).

Formula

T(n,0) = n and, for k = 1..A031346(n), T(n,k) = A031347(T(n,k-1)).

Example

Triangle begins:
  n\k|  0   1   2
  ---------------
   0 |  0;
   1 |  1;
   2 |  2;
   3 |  3;
   4 |  4;
   5 |  5;
   6 |  6;
   7 |  7;
   8 |  8;
   9 |  9;
  10 | 10,  0;
  11 | 11,  1;
  12 | 12,  2;
  13 | 13,  3;
  14 | 14,  4;
  15 | 15,  5;
  16 | 16,  6;
  17 | 17,  7;
  18 | 18,  8;
  19 | 19,  9;
  20 | 20,  0;
  21 | 21,  2;
  22 | 22,  4;
  23 | 23,  6;
  24 | 24,  8;
  25 | 25, 10,  0;
  ...

Mathematica

A381965row[n_] := NestWhileList[Times @@ IntegerDigits[#] &, n, # >= 10 &];
Array[A381965row, 50, 0]

Crossrefs

Cf. A031346 (row lengths - 1), A031347 (right border), A381966 (row sums).

Cf. A381962, A381963.

Sequence in context: A097462 A210944 A259434 * A329079 A306580 A320486

Adjacent sequences: A381962 A381963 A381964 * A381966 A381967 A381968

Keyword

nonn,tabf,base,easy

Author

Paolo Xausa, Mar 11 2025

Status

approved