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A278113
Triangle T(n,k) = A278112(n,A000040(k)) for 1 <= k <= A278114(n), read by rows.
4
1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 5, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 6, 5, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,2
COMMENTS
This triangle consists of those columns of A278112 that have prime index.
FORMULA
T(n,k) = floor(n*sqrt(2/prime(k))).
T(n,k) sqrt(A000040(k)) <= n sqrt(2) < (T(n,k)+1) sqrt(A000040(k)).
EXAMPLE
The first eight rows are:
1;
2, 1, 1, 1;
3, 2, 1, 1, 1, 1, 1;
4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1;
5, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
6, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
7, 5, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
8, 6, 5, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
MATHEMATICA
Table[Floor[n Sqrt[2/Prime@ k]], {n, 8}, {k, PrimePi[2 n^2]}] // Flatten (* Michael De Vlieger, Feb 17 2017 *)
PROG
(Magma)
A278112:=func<n, k|Isqrt(2*n^2 div k)>;
A278113_row:=func<n|[A278112(n, p):p in PrimesUpTo(2*n^2)]>;
&cat[A278113_row(n):n in[1..8]];
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Jason Kimberley, Feb 09 2017
STATUS
approved