A278113 Triangle T(n,k) = A278112(n,A000040(k)) for 1 <= k <= A278114(n), read by rows.

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.

Links

Jason Kimberley, Table of n, a(n) for n = 1..10126 (rows 1..46)

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

Cf. A000040, A277648, A278112, A278114, A278115, A278118.

Sequence in context: A319864 A072776 A077481 * A242012 A359165 A377364

Adjacent sequences: A278110 A278111 A278112 * A278114 A278115 A278116

Keyword

nonn,tabf,easy,changed

Author

Jason Kimberley, Feb 09 2017

Status

approved