A381963 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 digital sum of x (A007953).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 10, 1, 20, 2, 21, 3, 22, 4, 23, 5, 24, 6, 25, 7, 26, 8, 27, 9, 28, 10, 1, 29, 11, 2, 30, 3, 31, 4, 32, 5, 33, 6, 34, 7, 35, 8, 36, 9, 37, 10, 1, 38, 11, 2, 39, 12, 3

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..11648 (rows 0..4000 of triangle, flattened).

Formula

T(n,0) = n and, for k = 1..A031286(n), T(n,k) = A007953(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,  1;
  11 | 11,  2;
  12 | 12,  3;
  13 | 13,  4;
  14 | 14,  5;
  15 | 15,  6;
  16 | 16,  7;
  17 | 17,  8;
  18 | 18,  9;
  19 | 19, 10,  1;
  20 | 20,  2;
  ...

Mathematica

A381963row[n_] := NestWhileList[DigitSum, n, # >= 10 &];
Array[A381963row, 40, 0]

Crossrefs

Cf. A007953, A010888 (right border), A031286 (row lengths - 1), A381964 (row sums).

Cf. A381962, A381965.

Sequence in context: A067453 A384955 A203814 * A373211 A346393 A389875

Adjacent sequences: A381960 A381961 A381962 * A381964 A381965 A381966

Keyword

nonn,tabf,base,easy

Author

Paolo Xausa, Mar 11 2025

Status

approved