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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This triangle consists of those columns of A278112 that have prime index.

LINKS

Jason Kimberley, Table of n, a(i) for i = 1..10126 (T(n,k) for n = 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: A071178 A072776 A077481 * A242012 A086290 A136568

Adjacent sequences:  A278110 A278111 A278112 * A278114 A278115 A278116

KEYWORD

nonn,tabf,easy

AUTHOR

Jason Kimberley, Feb 09 2017

STATUS

approved

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Last modified December 15 03:08 EST 2017. Contains 296020 sequences.