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A258415 Array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (2 + 2^(n-1)*(6*k - 3 + 2*(-1)^n))/3, n,k >= 1. 1
1, 4, 3, 2, 8, 5, 14, 10, 12, 7, 6, 30, 18, 16, 9, 54, 38, 46, 26, 20, 11, 22, 118, 70, 62, 34, 24, 13, 214, 150, 182, 102, 78, 42, 28, 15, 86, 470, 278, 246, 134, 94, 50, 32, 17, 854, 598, 726, 406, 310, 166, 110, 58, 36, 19 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is a permutation of the natural numbers.

Theorem: Let v(y) denote the 2-adic valuation of y. For x an odd natural number, let F(x) = (3*x+1)/2^v(3*x+1) (see A075677). Row n of A is the set of all natural numbers m such that v(1+F(4*(2*m-1)-3)) = n.

LINKS

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

FORMULA

A(n,k) = (1 + A257499(n,k))/2.

EXAMPLE

Array begins:

.      1     3     5     7     9    11    13    15    17     19

.      4     8    12    16    20    24    28    32    36     40

.      2    10    18    26    34    42    50    58    66     74

.     14    30    46    62    78    94   110   126   142    158

.      6    38    70   102   134   166   198   230   262    294

.     54   118   182   246   310   374   438   502   566    630

.     22   150   278   406   534   662   790   918  1046   1174

.    214   470   726   982  1238  1494  1750  2006  2262   2518

.     86   598  1110  1622  2134  2646  3158  3670  4182   4694

.    854  1878  2902  3926  4950  5974  6998  8022  9046  10070

MATHEMATICA

(* Array: *)

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

(* Array antidiagonals flattened: *)

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

CROSSREFS

Cf. A005408, A008586, A017089 (rows 1-3).

Cf. A075677, A257480, A257499.

Sequence in context: A307648 A067016 A022295 * A132668 A018866 A021235

Adjacent sequences:  A258412 A258413 A258414 * A258416 A258417 A258418

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, May 29 2015

STATUS

approved

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Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)