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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).

%I A381963 #9 Mar 14 2025 21:20:04
%S A381963 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,
%T A381963 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,
%U A381963 4,32,5,33,6,34,7,35,8,36,9,37,10,1,38,11,2,39,12,3
%N 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).
%H A381963 Paolo Xausa, <a href="/A381963/b381963.txt">Table of n, a(n) for n = 0..11648</a> (rows 0..4000 of triangle, flattened).
%F A381963 T(n,0) = n and, for k = 1..A031286(n), T(n,k) = A007953(T(n,k-1)).
%e A381963 Triangle begins:
%e A381963   n\k|  0   1   2
%e A381963   ---------------
%e A381963    0 |  0;
%e A381963    1 |  1;
%e A381963    2 |  2;
%e A381963    3 |  3;
%e A381963    4 |  4;
%e A381963    5 |  5;
%e A381963    6 |  6;
%e A381963    7 |  7;
%e A381963    8 |  8;
%e A381963    9 |  9;
%e A381963   10 | 10,  1;
%e A381963   11 | 11,  2;
%e A381963   12 | 12,  3;
%e A381963   13 | 13,  4;
%e A381963   14 | 14,  5;
%e A381963   15 | 15,  6;
%e A381963   16 | 16,  7;
%e A381963   17 | 17,  8;
%e A381963   18 | 18,  9;
%e A381963   19 | 19, 10,  1;
%e A381963   20 | 20,  2;
%e A381963   ...
%t A381963 A381963row[n_] := NestWhileList[DigitSum, n, # >= 10 &];
%t A381963 Array[A381963row, 40, 0]
%Y A381963 Cf. A007953, A010888 (right border), A031286 (row lengths - 1), A381964 (row sums).
%Y A381963 Cf. A381962, A381965.
%K A381963 nonn,tabf,base,easy
%O A381963 0,3
%A A381963 _Paolo Xausa_, Mar 11 2025