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A206805
Position of 2^n when {2^j} and {3^k} are jointly ranked; complement of A206807.
6
1, 3, 4, 6, 8, 9, 11, 13, 14, 16, 17, 19, 21, 22, 24, 26, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 75, 76, 78, 79, 81, 83, 84, 86, 88, 89, 91, 92, 94, 96, 97, 99, 101, 102, 104, 106, 107
OFFSET
1,2
COMMENTS
The joint ranking is for j >= 1 and k >= 1, so that the sets {2^j} and {3^k} are disjoint. Not identical to A182774; e.g., A206805 contains 318 but A182774 does not.
LINKS
FORMULA
a(n) = n + floor(n*log_2(3)) (while A206807(n) = n + floor(n*log_3(2))).
EXAMPLE
The joint ranking begins with 2,3,4,8,9,16,27,32,64,81,128,243,256, so that
this sequence = (1,3,4,6,8,9,11,13,...),
A206807 = (2,5,7,10,12,...).
MATHEMATICA
f[n_] := 2^n; g[n_] := 3^n; z = 200;
c = Table[f[n], {n, 1, z}]; s = Table[g[n], {n, 1, z}];
j = Sort[Union[c, s]];
p[n_] := Position[j, f[n]]; q[n_] := Position[j, g[n]];
Flatten[Table[p[n], {n, 1, z}]] (* A206805 *)
Table[n + Floor[n*Log[3, 2]], {n, 1, 50}] (* A206805 *)
Flatten[Table[q[n], {n, 1, z}]] (* A206807 *)
Table[n + Floor[n*Log[2, 3]], {n, 1, 50}] (* A206807 *)
PROG
(PARI) a(n) = n + floor(n*log(2)/log(3)); \\ Jinyuan Wang, Jan 27 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 16 2012
STATUS
approved