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 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 digit-wise 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 end-of-row marker and makes indexing simpler and more natural. LINKS 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) = |n-k|). 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

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Last modified March 24 14:54 EDT 2023. Contains 361479 sequences. (Running on oeis4.)