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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
OFFSET
1,2
COMMENTS
Every positive integer is in exactly one of the sequences A322532, A322533, A322534.
LINKS
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
Sequence in context: A214858 A186276 A047383 * A314402 A133795 A247060
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 14 2018
STATUS
approved