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 A354438 Square array A(n, k), n, k >= 0, read by antidiagonals; the factorial base expansion of A(n, k) is obtained by adding componentwise and reducing modulo their radix the digits of the factorial base expansions of n and k. 2
 0, 1, 1, 2, 0, 2, 3, 3, 3, 3, 4, 2, 4, 2, 4, 5, 5, 5, 5, 5, 5, 6, 4, 0, 4, 0, 4, 6, 7, 7, 1, 1, 1, 1, 7, 7, 8, 6, 8, 0, 2, 0, 8, 6, 8, 9, 9, 9, 9, 3, 3, 9, 9, 9, 9, 10, 8, 10, 8, 10, 2, 10, 8, 10, 8, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The nonnegative integers together with A form an abelian group; A225901 gives inverse elements. Each row is a permutation of the nonnegative integers. LINKS Table of n, a(n) for n=0..77. Rémy Sigrist, Colored representation of the array A(n, k) for n, k < 7! (the hue is function of A(n, k), black pixels correspond to 0's) Index entries for sequences related to factorial base representation FORMULA A(n, k) = A(k, n). A(m, A(n, k)) = A(A(m, n), k). A(n, 0) = n. A(n, k) = 0 iff k = A225901(n). A(n, 1) = A004442(n). EXAMPLE Square array A(n, k) begins: n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ---+---------------------------------------------------------------- 0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1| 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 2| 2 3 4 5 0 1 8 9 10 11 6 7 14 15 16 17 3| 3 2 5 4 1 0 9 8 11 10 7 6 15 14 17 16 4| 4 5 0 1 2 3 10 11 6 7 8 9 16 17 12 13 5| 5 4 1 0 3 2 11 10 7 6 9 8 17 16 13 12 6| 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 7| 7 6 9 8 11 10 13 12 15 14 17 16 19 18 21 20 8| 8 9 10 11 6 7 14 15 16 17 12 13 20 21 22 23 9| 9 8 11 10 7 6 15 14 17 16 13 12 21 20 23 22 10| 10 11 6 7 8 9 16 17 12 13 14 15 22 23 18 19 11| 11 10 7 6 9 8 17 16 13 12 15 14 23 22 19 18 12| 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 13| 13 12 15 14 17 16 19 18 21 20 23 22 1 0 3 2 14| 14 15 16 17 12 13 20 21 22 23 18 19 2 3 4 5 15| 15 14 17 16 13 12 21 20 23 22 19 18 3 2 5 4 PROG (PARI) A(n, k, s=i->i+1) = { my (v=0, f=1, r); for (i=1, oo, if (n==0 && k==0, return (v), r=s(i); v+=f*((n+k)%r); f*=r; n\=r; k\=r)) } CROSSREFS Cf. A003987, A004442, A108731, A225901, A354470 (primorial base analog). Sequence in context: A307297 A307301 A307300 * A354470 A141692 A261097 Adjacent sequences: A354435 A354436 A354437 * A354439 A354440 A354441 KEYWORD nonn,base AUTHOR Rémy Sigrist, May 28 2022 STATUS approved

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Last modified September 22 00:10 EDT 2023. Contains 365503 sequences. (Running on oeis4.)