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A322534 Position of 2/3^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order. 3
1, 5, 8, 12, 15, 19, 23, 26, 30, 33, 37, 41, 44, 48, 51, 55, 58, 62, 66, 69, 73, 76, 80, 84, 87, 91, 94, 98, 101, 105, 109, 112, 116, 119, 123, 127, 130, 134, 137, 141, 144, 148, 152, 155, 159, 162, 166, 170, 173, 177, 180, 184, 188, 191, 195, 198, 202, 205 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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: A214858 A186276 A047383 * A314402 A133795 A247060

Adjacent sequences: A322531 A322532 A322533 * A322535 A322536 A322537

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 14 2018

STATUS

approved

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Last modified January 31 17:49 EST 2023. Contains 359980 sequences. (Running on oeis4.)