A206805 Position of 2^n when {2^j} and {3^k} are jointly ranked; complement of A206807.
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
Keywords
Examples
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,...).
Links
- Jinyuan Wang, Table of n, a(n) for n = 1..1000
Programs
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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 *) -
PARI
a(n) = n + floor(n*log(2)/log(3)); \\ Jinyuan Wang, Jan 27 2020
Formula
a(n) = n + floor(n*log_2(3)) (while A206807(n) = n + floor(n*log_3(2))).
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