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 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-François 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

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