A292965 - OEIS

%I #6 Oct 06 2017 21:34:21

%S 1,2,5,3,8,10,4,12,16,17,6,15,22,26,23,7,20,30,35,36,31,9,25,38,46,50,

%T 47,39,11,29,45,58,64,65,59,48,13,34,54,70,78,84,79,71,56,14,41,63,83,

%U 95,103,104,97,86,67,18,44,73,94,113,123,127,124,115,99

%N Rectangular array by antidiagonals: T(n,m) = rank of n*(Pi + m) when all the numbers k*(Pi+h), for k >= 1, h >= 0, are jointly ranked.

%C Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.

%H Clark Kimberling, <a href="/A292965/b292965.txt">Antidiagonals n=1..60, flattened</a>

%F T(n,m) = Sum_{k=1...[n + m*n/Pi]} [1 - Pi + n*(Pi + m)/k], where [ ]=floor.

%F Northwest corner:

%F 1      2     3     4     6     7

%F 5      8     12    15    20    25

%F 10     16    22    30    38    45

%F 17     26    35    46    58    70

%F 23     36    50    64    78    95

%F 31     47    65    84    103   123

%F 39     59    79    104   127   153

%F The numbers k*(Pi+h), approximately:

%F (for k=1):   3.141   4.141   5.141 ...

%F (for k=2):   6.283   8.283   10.283 ...

%F (for k=3):   9.424   12.424  15.424 ...

%F Replacing each by its rank gives

%F 1    2    3

%F 5    8    12

%F 10   16   22

%t r = Pi; z = 12;

%t t[n_, m_] := Sum[Floor[1 - r + n*(r + m)/k], {k, 1, Floor[n + m*n/r]}];

%t u = Table[t[n, m], {n, 1, z}, {m, 0, z}]; TableForm[u]  (* A292965 array *)

%t Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten  (* A292965 sequence *)

%Y Cf. A182801.

%K nonn,easy,tabl

%O 1,2

%A _Clark Kimberling_, Oct 06 2017