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 A323376 Square array read by ascending antidiagonals: T(n,k) is the multiplicative order of the n-th prime modulo the k-th prime, or 0 if n = k, n >= 1, k >= 1. 1
 0, 1, 2, 1, 0, 4, 1, 2, 4, 3, 1, 1, 0, 6, 10, 1, 2, 4, 6, 5, 12, 1, 1, 1, 0, 5, 3, 8, 1, 2, 4, 3, 10, 4, 16, 18, 1, 1, 4, 2, 0, 12, 16, 18, 11, 1, 2, 2, 6, 10, 12, 16, 9, 11, 28, 1, 2, 4, 6, 10, 0, 16, 3, 22, 28, 5, 1, 1, 2, 3, 10, 6, 4, 3, 22, 14, 30, 36 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The maximum element in the k-th column is prime(k) - 1. By Dirichlet's theorem on arithmetic progressions, all divisors of prime(k) - 1 occur infinitely many times in the n-th column. LINKS Alois P. Heinz, Antidiagonals n = 1..200, flattened FORMULA T(n,k) = A250211(prime(n), prime(k)). EXAMPLE Table begins | k | 1 2 3 4 5 6 7 8 9 10 ... n | p() | 2 3 5 7 11 13 17 19 23 29 ... ---+-----+---------------------------------------- 1 | 2 | 0, 2, 4, 3, 10, 12, 8, 18, 11, 28, ... 2 | 3 | 1, 0, 4, 6, 5, 3, 16, 18, 11, 28, ... 3 | 5 | 1, 2, 0, 6, 5, 4, 16, 9, 22, 14, ... 4 | 7 | 1, 1, 4, 0, 10, 12, 16, 3, 22, 7, ... 5 | 11 | 1, 2, 1, 3, 0, 12, 16, 3, 22, 28, ... 6 | 13 | 1, 1, 4, 2, 10, 0, 4, 18, 11, 14, ... 7 | 17 | 1, 2, 4, 6, 10, 6, 0, 9, 22, 4, ... 8 | 19 | 1, 1, 2, 6, 10, 12, 8, 0, 22, 28, ... 9 | 23 | 1, 2, 4, 3, 1, 6, 16, 9 , 0, 7, ... 10 | 29 | 1, 2, 2, 1, 10, 3, 16, 18, 11, 0, ... ... MAPLE A:= (n, k)-> `if`(n=k, 0, (p-> numtheory[order](p(n), p(k)))(ithprime)): seq(seq(A(1+d-k, k), k=1..d), d=1..14); # Alois P. Heinz, Feb 06 2019 MATHEMATICA T[n_, k_] := If[n == k, 0, MultiplicativeOrder[Prime[n], Prime[k]]]; Table[T[n, k], {n, 1, 10}, {k, 1, 10}] (* Peter Luschny, Jan 20 2019 *) PROG (PARI) T(n, k) = if(n==k, 0, znorder(Mod(prime(n), prime(k)))) CROSSREFS Cf. A250211. Cf. A014664 (1st row), A062117 (2nd row), A211241 (3rd row), A211243 (4th row), A039701 (2nd column). Cf. A226367 (lower diagonal), A226295 (upper diagonal). Sequence in context: A334044 A143724 A143425 * A166555 A136329 A122073 Adjacent sequences: A323373 A323374 A323375 * A323377 A323378 A323379 KEYWORD nonn,tabl AUTHOR Jianing Song, Jan 12 2019 STATUS approved

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Last modified December 2 16:29 EST 2023. Contains 367525 sequences. (Running on oeis4.)