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 A159861 Square array A(m,n), m>=1, n>=1, read by antidiagonals: A(m,1)=1, A(m,n) is the rank with respect to m of the concatenation of all preceding terms in row m, and the rank of S with respect to m is floor ((S+m-1)/m). 2
 1, 1, 1, 11, 1, 1, 1111, 6, 1, 1, 11111111, 58, 4, 1, 1, 1111111111111111, 5829, 38, 3, 1, 1, 11111111111111111111111111111111, 58292915, 3813, 29, 3, 1, 1, 1111111111111111111111111111111111111111111111111111111111111111, 5829291479146458, 38127938, 2833, 23, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Antidiagonals n = 1..12, flattened EXAMPLE A(3,4) = 38, because A(3,1).A(3,2).A(3,3) = 114, and the rank of 114 with respect to 3 is floor(116/3) = 38. Square array A(m,n) begins: 1, 1, 11, 1111, 11111111, 1111111111111111, ... 1, 1, 6, 58, 5829, 58292915, ... 1, 1, 4, 38, 3813, 38127938, ... 1, 1, 3, 29, 2833, 28323209, ... 1, 1, 3, 23, 2265, 22646453, ... 1, 1, 2, 19, 1870, 18698645, ... MAPLE R:= (S, m)-> iquo(S+m-1, m): A:= proc(m, n) option remember; `if`(n=1, 1, R(parse(cat(seq(A(m, j), j=1..n-1))), m)) end: seq(seq(A(m, d-m), m=1..d-1), d=1..10); MATHEMATICA R[S_, m_] := Quotient[S + m - 1, m]; A[m_, n_] := If[n == 1, 1, R[ToExpression@StringJoin[ToString /@ Table[A[m, j], {j, 1, n - 1}]], m]]; Table[Table[A[m, d - m], {m, 1, d - 1}], {d, 1, 10}] // Flatten (* Jean-François Alcover, Feb 13 2023, after Maple code *) CROSSREFS Row m=2 gives: A156147. Main diagonal gives: A159862. Cf. A156146, A010783. Sequence in context: A173006 A015125 A290552 * A010197 A010196 A039617 Adjacent sequences: A159858 A159859 A159860 * A159862 A159863 A159864 KEYWORD easy,nonn,tabl,base AUTHOR Eric Angelini and Alois P. Heinz, Apr 24 2009 STATUS approved

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Last modified September 18 20:16 EDT 2024. Contains 376002 sequences. (Running on oeis4.)