A233572 In balanced ternary notation, if prepending same numbers of zeros, reverse digits of a(n) equals to -a(n)

0, 2, 6, 8, 18, 20, 24, 26, 32, 54, 56, 60, 72, 78, 80, 96, 104, 146, 162, 164, 168, 180, 182, 216, 224, 234, 240, 242, 260, 288, 302, 312, 320, 338, 416, 438, 486, 488, 492, 504, 540, 546, 560, 648, 656, 672, 702, 720, 726, 728, 780, 800, 864, 896, 906, 936

Offset

1,2

Comments

A233571 is a subset of this sequence.

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

Example

In balanced ternary notation, 18 = (1T00)_bt, where we use T to represent -1.  Patching two zeros before it, (1T00)_bt=(001T00)_bt.  The reverse digits of (001T00)_bt is (00T100)_bt = -18.  So 18 is in this sequence.

Mathematica

BTDigits[m_Integer, g_] :=
Module[{n = m, d, sign, t = g},
  If[n != 0, If[n > 0, sign = 1, sign = -1; n = -n];
   d = Ceiling[Log[3, n]]; If[3^d - n <= ((3^d - 1)/2), d++];
   While[Length[t] < d, PrependTo[t, 0]]; t[[Length[t] + 1 - d]] = sign;
   t = BTDigits[sign*(n - 3^(d - 1)), t]]; t];
BTrteQ[n_Integer] :=
Module[{t, trim = n/3^IntegerExponent[n, 3]},
  t = BTDigits[trim, {0}]; DeleteDuplicates[t + Reverse[t]] == {0}];
sb = Select[Range[0, 950], BTrteQ[#] &]

Crossrefs

Cf. A002113, A061917, A006995, A057890, A134027, A233010, A233571

Sequence in context: A360264 A325686 A053355 * A370864 A005823 A259026

Adjacent sequences: A233569 A233570 A233571 * A233573 A233574 A233575

Keyword

nonn,base

Author

Lei Zhou, Dec 13 2013

Status

approved