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A278117
Irregular triangle T(n,k) = A278115(n,k) for 1 <= k <= A278116(n), read by rows.
2
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.
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
Sequence in context: A328487 A083003 A364130 * A193976 A264244 A292930
KEYWORD
nonn,tabf,easy
AUTHOR
Jason Kimberley, Feb 12 2017
STATUS
approved