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A322533 Position of 1/3^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order. 3
3, 7, 10, 14, 17, 21, 25, 28, 32, 35, 39, 43, 46, 50, 53, 57, 60, 64, 68, 71, 75, 78, 82, 86, 89, 93, 96, 100, 103, 107, 111, 114, 118, 121, 125, 129, 132, 136, 139, 143, 146, 150, 154, 157, 161, 164, 168, 172, 175, 179, 182, 186, 190, 193, 197, 200, 204 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer is in exactly one of the sequences A322532, A322533, A322534.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

FORMULA

Position of 1/2^n: n + floor(n log(2)/log(3)) + floor((n + 1) log(2)/log(3))

Position of 1/3^n: 2n - 2 + floor(n log(3)/log(2))

Position of 2/3^n: 2n + floor(n log(3)/log(2))

EXAMPLE

In the decreasing sequence 2/3, 1/2, 1/3, 1/4, 2/9, 1/8, 1/9, 2/27, 1/16, ..., the positions of 1/2, 1/4, 1/8, 1/6, are 2,4,6,9; the positions of 1/3, 1/9, 1/27,... are 3,7,10,14,...; the positions of 2/3, 2/9,2/27,... are 1,5,8,12,...

MATHEMATICA

a[n_] := n + Floor[n Log[2]/Log[3]] + Floor[(n + 1) Log[2]/Log[3]];

b[n_] := 2 n - 2 + Floor[n Log[3]/Log[2]];

c[n_] := 2 n + Floor[n Log[3]/Log[2]];

Table[a[n], {n, 1, 120}] (* A322532 *)

Table[b[n], {n, 1, 120}] (* A322533 *)

Table[c[n], {n, 1, 120}] (* A322534 *)

CROSSREFS

Cf. A322532, A322534.

Sequence in context: A047355 A248522 A098005 * A189999 A310188 A171983

Adjacent sequences: A322530 A322531 A322532 * A322534 A322535 A322536

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 14 2018

STATUS

approved

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Last modified January 27 17:42 EST 2023. Contains 359845 sequences. (Running on oeis4.)