cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 11 2025

Keywords

Examples

			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;
  ...
		

Crossrefs

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

Programs

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

Formula

T(n,0) = n and, for k = 1..A031286(n), T(n,k) = A007953(T(n,k-1)).
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