

A322532


Position of 1/2^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order.


3



2, 4, 6, 9, 11, 13, 16, 18, 20, 22, 24, 27, 29, 31, 34, 36, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59, 61, 63, 65, 67, 70, 72, 74, 77, 79, 81, 83, 85, 88, 90, 92, 95, 97, 99, 102, 104, 106, 108, 110, 113, 115, 117, 120, 122, 124, 126, 128, 131, 133, 135, 138
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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. A322533, A322534.
Sequence in context: A329826 A330908 A327213 * A284365 A059545 A187339
Adjacent sequences: A322529 A322530 A322531 * A322533 A322534 A322535


KEYWORD

nonn


AUTHOR

Clark Kimberling, Dec 14 2018


STATUS

approved



