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A206814 Position of 5^n in joint ranking of {2^i}, {3^j}, {5^k}. 3
4, 8, 13, 18, 23, 27, 33, 37, 42, 47, 52, 56, 62, 66, 70, 76, 80, 85, 90, 95, 99, 105, 109, 114, 119, 124, 128, 134, 138, 142, 147, 152, 157, 161, 167, 171, 176, 181, 186, 190, 196, 200, 204, 210, 214, 219, 224, 229, 233, 239, 243, 248, 253, 258, 262 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..55.

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=(1,3,5,7,10,11,14,...)

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, A206812, A206813.

Sequence in context: A127264 A189370 A190054 * A130236 A198464 A034856

Adjacent sequences:  A206811 A206812 A206813 * A206815 A206816 A206817

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 17 2012

STATUS

approved

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Last modified April 21 01:47 EDT 2014. Contains 240824 sequences.