

A330238


Triangle T(n,k): concatenate the absolute differences of the digits of n and k (the smaller one padded with leading zeros); n >= k >= 1.


3



0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 0, 11, 10, 11, 12, 13, 14, 15, 16, 17, 2, 1, 0, 12, 11, 10, 11, 12, 13, 14, 15, 16, 3, 2, 1, 0, 13, 12, 11, 10, 11, 12, 13, 14, 15, 4, 3, 2, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

A digitwise analog of A049581.
The binary operator T: N x N > N is commutative, so we need only the lower half of the symmetric square table A330238 or A330240 (including n, k = 0). Also, 0 is the neutral element: T(x,0) = x for all x, therefore we omit row & column 0. The trivial diagonal T(x,x) = 0 could also be omitted but serves as an endofrow marker and makes indexing simpler and more natural.


LINKS

Table of n, a(n) for n=1..105.
Eric Angelini, The box ■ operation, personal blog "Cinquante signes", and post to the SeqFan list, Dec 06 2019.


EXAMPLE

The triangle starts as follows:
n  k=1 2 3 4 5 6 7 8 9 10 11
+
1  0,
2  1, 0,
3  2, 1, 0,
4  3, 2, 1, 0,
5  4, 3, 2, 1, 0,
6  5, 4, 3, 2, 1, 0,
7  6, 5, 4, 3, 2, 1, 0,
8  7, 6, 5, 4, 3, 2, 1, 0,
9  8, 7, 6, 5, 4, 3, 2, 1, 0,
10  11, 12, 13, 14, 15, 16, 17, 18, 19, 0,
11  10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 0,
12  11, 10, 11, 12, 13, 14, 15, 16, 17, 2, 1, 0,
(...)


PROG

(PARI) A330238(n, k)=fromdigits(digits(n)abs(Vec(digits(k), logint(n, 10)1))) \\ see A330240 for a more general function not limited to 1 <= k <= n


CROSSREFS

Cf. A330237 (same as a square array read by antidiagonals), A330240 (idem, including row & column 0), A049581 (T(n,k) = nk).
Sequence in context: A025660 A025677 A025651 * A025670 A122200 A025646
Adjacent sequences: A330235 A330236 A330237 * A330239 A330240 A330241


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Dec 06 2019


STATUS

approved



