A278117 Irregular triangle T(n,k) = A278115(n,k) for 1 <= k <= A278116(n), read by rows.

2, 8, 3, 18, 12, 5, 32, 27, 20, 50, 48, 45, 28, 72, 48, 45, 98, 75, 128, 108, 162, 147, 125, 112, 99, 200, 192, 180, 175, 242, 192, 180, 175, 288, 243, 338, 300, 392, 363, 320, 450, 432, 405, 512, 507, 500, 448, 396, 578, 507, 500, 648, 588, 722, 675, 800, 768, 720

Offset

1,1

Comments

Each row is the longest strictly decreasing prefix of the corresponding row of A278115.

Links

Jason Kimberley, Table of i, a(i) for i = 1..10104 (T(n,k) for n = 1..3333)

Example

The first six rows are:
2;
8, 3;
18, 12, 5;
32, 27, 20;
50, 48, 45, 28;
72, 48, 45;

Mathematica

Map[Take[#, 1 + Length@ TakeWhile[Differences@ #, # < 0 &]] &, #] &@ Table[# Floor[n Sqrt[2/#]]^2 &@ Prime@ k, {n, 20}, {k, PrimePi[2 n^2]}] // Flatten (* Michael De Vlieger, Feb 17 2017 *)

Prog

(Magma)
A278112:=func<n, k|Isqrt(2*n^2 div k)>;
A278115_row:=func<n|[A278112(n, p)^2*p:p in PrimesUpTo(2*n^2)]>;
A278117_row:=func<n|(exists(dec){row[1..j]:j in[1..#row-1]|row[j]le row[j+1]}select dec else row) where row is A278115_row(n) >;
&cat[A278117_row(n):n in[1..20]];

Crossrefs

Cf. A278103, A278118.

Sequence in context: A328487 A083003 A364130 * A193976 A264244 A292930

Adjacent sequences: A278114 A278115 A278116 * A278118 A278119 A278120

Keyword

nonn,tabf,easy

Author

Jason Kimberley, Feb 12 2017

Status

approved