cp's OEIS Frontend

A374448 Irregular table T(n, k), n >= 0, 0 <= k < A089898(n), read by rows; the n-th row lists the numbers m in the range 0..n such that m and n-m can be added without carries in base 10.

%I A374448 #8 Jul 13 2024 11:10:13
%S A374448 0,0,1,0,1,2,0,1,2,3,0,1,2,3,4,0,1,2,3,4,5,0,1,2,3,4,5,6,0,1,2,3,4,5,
%T A374448 6,7,0,1,2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,9,0,10,0,1,10,11,0,1,2,10,11,
%U A374448 12,0,1,2,3,10,11,12,13,0,1,2,3,4,10,11,12,13,14
%N A374448 Irregular table T(n, k), n >= 0, 0 <= k < A089898(n), read by rows; the n-th row lists the numbers m in the range 0..n such that m and n-m can be added without carries in base 10.
%C A374448 The n-th row lists the numbers m such that for any k > 0, the k-th rightmost digit of m is <= the k-th rightmost digit of n.
%H A374448 Rémy Sigrist, <a href="/A374448/b374448.txt">Table of n, a(n) for n = 0..9077</a> (rows for n = 0..200 flattened)
%F A374448 T(n, 0) = 0.
%F A374448 T(n, A089898(n)-1) = n.
%F A374448 T(n, k) + T(n, A089898(n)-1-k) = n.
%F A374448 T(10*n, k) = 10*T(n, k).
%e A374448 Table T(n, k) begins:
%e A374448   n   n-th row
%e A374448   --  ---------------------------------
%e A374448    0  0
%e A374448    1  0, 1
%e A374448    2  0, 1, 2
%e A374448    3  0, 1, 2, 3
%e A374448    4  0, 1, 2, 3, 4
%e A374448    5  0, 1, 2, 3, 4, 5
%e A374448    6  0, 1, 2, 3, 4, 5, 6
%e A374448    7  0, 1, 2, 3, 4, 5, 6, 7
%e A374448    8  0, 1, 2, 3, 4, 5, 6, 7, 8
%e A374448    9  0, 1, 2, 3, 4, 5, 6, 7, 8, 9
%e A374448   10  0, 10
%e A374448   11  0, 1, 10, 11
%e A374448   12  0, 1, 2, 10, 11, 12
%e A374448   13  0, 1, 2, 3, 10, 11, 12, 13
%e A374448   14  0, 1, 2, 3, 4, 10, 11, 12, 13, 14
%o A374448 (PARI) T(n, k, base = 10) = { my (v = 0, p = 1, d, t); while (n, d = n % base; n \= base; t = k % (d+1); k \= (d+1); v += t * p; p *= base;); return (v); }
%Y A374448 Cf. A002262, A089898, A295989 (base-2 analog).
%K A374448 nonn,base,easy,tabf
%O A374448 0,6
%A A374448 _Rémy Sigrist_, Jul 08 2024