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A257852 Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n,k) = (2^n*(6*k - 3 - 2*(-1)^n) - 1)/3, n,k >= 1. 0
3, 1, 7, 13, 9, 11, 5, 29, 17, 15, 53, 37, 45, 25, 19, 21, 117, 69, 61, 33, 23, 213, 149, 181, 101, 77, 41, 27, 85, 469, 277, 245, 133, 93, 49, 31, 853, 597, 725, 405, 309, 165, 109, 57, 35, 341, 1877, 1109, 981, 533, 373, 197, 125, 65, 39 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence is a permutation of the odd natural numbers.

Let N_1 denote the set of odd natural numbers, and let |y|_2 denote 2-adic valuation of y. Define the map F : N_1 -> N_1 by F(x) = (3*x + 1)/2^|3*x+1|_2 (cf. A075677). Then row n of A is the set of all x in N_1 for which |3*x + 1|_2 = n. Hence F(A(n,k)) = 6*k - 3 - 2*(-1)^n.

LINKS

Table of n, a(n) for n=1..55.

MATHEMATICA

(* Array: *)

Grid[Table[(2^n*(6*k - 3 - 2*(-1)^n) - 1)/3, {n, 10}, {k, 10}]]

(* Array antidiagonals flattened: *)

Flatten[Table[(2^(n - k + 1)*(6*k - 3 - 2*(-1)^(n - k + 1)) - 1)/ 3, {n, 10}, {k, n}]]

CROSSREFS

Cf. A006370, A075677, A096773.

Sequence in context: A218592 A113647 A161380 * A051927 A322069 A194595

Adjacent sequences:  A257849 A257850 A257851 * A257853 A257854 A257855

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, Jul 12 2015

STATUS

approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)