login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A240400 Numbers n having a partition into distinct parts of form 3^k-2^k. 4
0, 1, 5, 6, 19, 20, 24, 25, 65, 66, 70, 71, 84, 85, 89, 90, 211, 212, 216, 217, 230, 231, 235, 236, 276, 277, 281, 282, 295, 296, 300, 301, 665, 666, 670, 671, 684, 685, 689, 690, 730, 731, 735, 736, 749, 750, 754, 755, 876, 877, 881, 882, 895, 896, 900, 901 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers n such that there are partitions into distinct parts from A001047. - Joerg Arndt, Apr 06 2014

Based on casting binary numbers as ternary numbers. - Jon Perry, Apr 12 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

FORMULA

A241759(a(n)) > 0. - Reinhard Zumkeller, Apr 28 2014

Recursive formula: For n >= 1, a(1)=1 then a(n) = n + 3*a(floor(n/2)). Sum: a(n) = Sum_{k=0..floor(log_2(n))} 3^k*floor(n/2^k). - Benoit Cloitre, Apr 06 2019

EXAMPLE

25 = 19 + 5 + 1 so 25 is in the sequence.

MATHEMATICA

max = 1000; nmax = FindRoot[3^n - 2^n == max, {n, 1}][[1, 2]] // Ceiling; partitions = Select[Table[{3^n - 2^n}, {n, 1, nmax}], (First[#] <= max)&] //. {a___, b_List, c___, d_List, e___} /; Total[b] + Total[d] <= max && FreeQ[p = {a, b, c, d, e}, (j = Join[b, d] // Sort)] && j == Union[j] :> Union[Append[p, j]]; Join[{0}, Total /@ partitions // Sort] (* Jean-Fran├žois Alcover, Apr 16 2014 *)

PROG

(JavaScript)

function trimArray(arr) {

var c, i, j;

c = new Array();

for (j = 0; j < arr.length; j++) c[j] = arr[j];

c.sort(function(a, b) {return a - b; });

i = -1;

while(i++ < c.length - 1)

if (c[i] == c[i + 1]) c.splice(i--, 1);

return c;

}

a = new Array();

for (i = 0; i < 10; i++)

a[i] = Math.pow(3, i) - Math.pow(2, i);

b = new Array();

bc = 0;

for (j = 0; j < 130; j++) {

c = 0;

s = j.toString(2);

sl = s.length;

for (k = 0; k < sl; k++) if (s.charAt(k) == 1) c += a[k];

b[bc++] = c;

}

b = trimArray(b);

document.write(b);

(Haskell)

a240400 n = a240400_list !! (n-1)

a240400_list = filter ((> 0) . a241759) [0..]

-- Reinhard Zumkeller, Apr 28 2014

(PARI)

a(n)=if(n<2, n%2, n+3*a(floor(n/2)))

CROSSREFS

Cf. A241783 (complement).

Cf. A001047, A005187, A080277, A241759.

Sequence in context: A333405 A063445 A257331 * A031448 A290254 A163772

Adjacent sequences:  A240397 A240398 A240399 * A240401 A240402 A240403

KEYWORD

nonn

AUTHOR

Jon Perry, Apr 04 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 14 01:29 EDT 2021. Contains 345016 sequences. (Running on oeis4.)