A254312 Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (2^a(n)*(6*k - (3 - (-1)^a(n))*(1 - (-1)^n)/2) - 2^n + 4)/6, n,k >= 1, where {a(n)} is the Beatty sequence A117630 defined by a(n) = floor(n*log(3)/log(3/2)).

3, 32, 7, 170, 64, 11, 1022, 426, 96, 15, 2726, 2046, 682, 128, 19, 65526, 10918, 3070, 938, 160, 23, 174742, 131062, 19110, 4094, 1194, 192, 27, 2097110, 436886, 196598, 27302, 5118, 1450, 224, 31, 11184726, 4194262, 699030, 262134, 35494, 6142, 1706, 256, 35

Offset

1,1

Comments

Conjecture: The array A contains without duplication all natural numbers m such that m < S(m), where the function S is as defined in A257480; i.e., the sequence is a permutation of A254311.

Links

Table of n, a(n) for n=1..45.

Example

Array A begins:
.         3       7      11      15       19       23       27       31
.        32      64      96     128      160      192      224      256
.       170     426     682     938     1194     1450     1706     1962
.      1022    2046    3070    4094     5118     6142     7166     8190
.      2726   10918   19110   27302    35494    43686    51878    60070
.     65526  131062  196598  262134   327670   393206   458742   524278
.    174742  436886  699030  961174  1223318  1485462  1747606  2009750
.   2097110 4194262 6291414 8388566 10485718 12582870 14680022 16777174

Mathematica

(* Array antidiagonals flattened: *)
a[n_] := Floor[n*Log[3/2, 3]]; A254312[n_, k_] := (2^a[n]*(6*k - (3 - (-1)^a[n])*(1 - (-1)^n)/2) - 2^n + 4)/6; Flatten[Table[A254312[n - k + 1, k], {n, 9}, {k, n}]]

Crossrefs

Cf. A117630, A254311, A257480.

Cf. A004767, A174312 (rows 1 and 2).

Sequence in context: A173649 A210648 A119937 * A304048 A324223 A197368

Adjacent sequences: A254309 A254310 A254311 * A254313 A254314 A254315

Keyword

nonn,tabl

Author

L. Edson Jeffery, May 03 2015

Status

approved