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A259016 A(n,k) = k-th pi-based antiderivative of n; square array A(n,k), n>=0, k>=0, read by antidiagonals. 9
0, 0, 1, 0, 2, 2, 0, 3, 3, 3, 0, 5, 5, 5, 4, 0, 11, 11, 11, 4, 5, 0, 10, 10, 10, 4, 11, 6, 0, 29, 29, 29, 4, 10, 13, 7, 0, 78, 78, 78, 4, 29, 41, 6, 8, 0, 141, 141, 141, 4, 78, 35, 13, 19, 9, 0, 266, 266, 266, 4, 141, 38, 41, 15, 23, 10, 0, 147, 147, 147, 4, 266, 163, 35, 14, 83, 29, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
A(n,k) = min { m >= 0 : A258851^k(m) = n }.
A258850(A(n,k),k) = n.
A(n,k) <= A000040^k(n) for n>0.
EXAMPLE
A(5,3) = 29 -> 10 -> 11 -> 5.
A(5,4) = 78 -> 127 -> 31 -> 11 -> 5.
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 2, 3, 5, 11, 10, 29, 78, 141, 266, ...
2, 3, 5, 11, 10, 29, 78, 141, 266, 147, ...
3, 5, 11, 10, 29, 78, 141, 266, 147, 194, ...
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...
5, 11, 10, 29, 78, 141, 266, 147, 194, 1181, ...
6, 13, 41, 35, 38, 163, 138, 253, 346, 1383, ...
7, 6, 13, 41, 35, 38, 163, 138, 253, 346, ...
8, 19, 15, 14, 43, 191, 201, 217, 1113, 1239, ...
9, 23, 83, 431, 3001, 27457, 10626, 112087, 87306, 172810, ...
MAPLE
with(numtheory):
d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
A:= proc() local t, A; t, A:= proc()-1 end, proc()-1 end;
proc(n, k) local h;
while A(n, k) = -1 do
t(k):= t(k)+1; h:= (d@@k)(t(k));
if A(h, k) = -1 then A(h, k):= t(k) fi
od; A(n, k)
end
end():
seq(seq(A(n, h-n), n=0..h), h=0..12);
MATHEMATICA
d[n_] := If[n == 0, 0, n*Total[Last[#]*PrimePi[First[#]]/First[#]& /@ FactorInteger[n]]];
A[n_, k_] := For[m = 0, True, m++, If[Nest[d, m, k] == n, Return[m]]];
Table[A[n, k-n], {k, 0, 12}, {n, 0, k}] // Flatten (* Jean-François Alcover, Mar 20 2017 *)
CROSSREFS
Columns k=0-3 give: A001477, A258861, A258862, A258995.
Rows n=0,1,4,7,8,9 give: A000004, A258975, A010709, A259168, A259169, A259170.
Sequence in context: A288530 A295675 A135356 * A216504 A216673 A363532
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 16 2015
STATUS
approved

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Last modified May 18 16:58 EDT 2024. Contains 372664 sequences. (Running on oeis4.)