

A206812


Position of 2^n in joint ranking of {2^i}, {3^j}, {5^k}.


4



1, 3, 5, 7, 10, 11, 14, 16, 17, 20, 21, 24, 26, 28, 30, 32, 34, 36, 38, 40, 43, 44, 46, 49, 50, 53, 55, 57, 59, 60, 63, 65, 67, 69, 72, 73, 75, 77, 79, 82, 83, 86, 88, 89, 92, 94, 96, 98, 100, 102, 104, 106, 108, 111, 112, 115, 116, 118, 121, 122, 125, 127, 129
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OFFSET

1,2


COMMENTS

The exponents i,j,k range through the set N of positive integers, so that the position sequences (A206812 for 2^n, A206813 for 3^n, A206814 for 5^n) partition N.


LINKS

Table of n, a(n) for n=1..63.


FORMULA

A205812(n) = n + [n*log(base 3)(2)] + [n*log(base 5)(2)],
A205813(n) = n + [n*log(base 2)(3)] + [n*log(base 5)(3)],
A205814(n) = n + [n*log(base 2)(5)] + [n*log(base 3)(5)],
where []=floor.


EXAMPLE

The joint ranking begins with 2,3,4,5,8,9,16,25,27,32,64,81,125,128,243,256, so that
A205812=(1,3,5,7,10,11,...)
A205813=(2,6,9,12,15,...)
A205814=(4,8,13,18,23,...)


MATHEMATICA

f[1, n_] := 2^n; f[2, n_] := 3^n;
f[3, n_] := 5^n; z = 1000;
d[n_, b_, c_] := Floor[n*Log[b, c]];
t[k_] := Table[f[k, n], {n, 1, z}];
t = Sort[Union[t[1], t[2], t[3]]];
p[k_, n_] := Position[t, f[k, n]];
Flatten[Table[p[1, n], {n, 1, z/8}]] (* A206812 *)
Table[n + d[n, 3, 2] + d[n, 5, 2],
{n, 1, 50}] (* A206812 *)
Flatten[Table[p[2, n], {n, 1, z/8}]] (* A206813 *)
Table[n + d[n, 2, 3] + d[n, 5, 3],
{n, 1, 50}] (* A206813 *)
Flatten[Table[p[3, n], {n, 1, z/8}]] (* A206814 *)
Table[n + d[n, 2, 5] + d[n, 3, 5],
{n, 1, 50}] (* A206814 *)


CROSSREFS

Cf. A206805, A206813, A206814.
Sequence in context: A189171 A189220 A189009 * A189372 A108052 A046868
Adjacent sequences: A206809 A206810 A206811 * A206813 A206814 A206815


KEYWORD

nonn


AUTHOR

Clark Kimberling, Feb 17 2012


STATUS

approved



