A089184 A coding semi-palindromic sequence made by converting a zero containing limited digit set palindromic sequence to a fraction and then converting back to an continued fraction array and making the sequence up from the result.

1, 22, 111, 4444, 33333, 333333, 3333333, 13333133, 133331133, 3323333233, 31133331133, 333343333433, 3333333333333, 33333333333333, 333333333333333, 3313333333313333, 31133333333113333, 333323333333323333

Offset

2,2

Links

Table of n, a(n) for n=2..19.

Formula

a(n) = CodeContinuedfraction[Palindromic number[n]]

Mathematica

Clear [a, b, c, d, e, f, g, m] (* these continued fraction functions are given in the Mathematica documentation*) CF[r0_?NumericQ, n_Integer?NonNegative] := Module[{l = {}, r = r0, a}, Do[ a = Floor[r]; (* integer part *) AppendTo[l, a]; r = r - a; (* fractional part; 0 <= r < 1 *) If[ r == 0, Break[] ]; r = 1/r; (* r > 1 *), {n}]; l ] CFValue[l_List] := Fold[ 1/#1 + #2&, Infinity, Reverse[l] ] digits=50 c[1]=1 c[2]=0 c[3]=2 c[0]=3 (* general Palindromic continued fraction generator for length m-1*) a[m_]=Delete[Table[If [ Floor[m/2]-n>=0, c[ Mod[n, 4]], c[Mod[m-n, 4]]], {n, 1, m}], m] (* make the fraction from the palindromic array*) e=Table[CFValue[Flatten[Table[a[m], {k, 1, digits}]]], {m, 2, digits}]; (* get the new semi- Palindromic continued fraction array with zeros eliminated*) f[n_]=CF[e[[n]], digits]; (* create new semi-palindromic sequence from the continued fraction array*) g=Table[Sum[f[m][[i]]*10^(i-1), {i, 1, m-1}], {m, 2, digits-1}]

Crossrefs

Cf. A007907.

Sequence in context: A084013 A083123 A084017 * A214216 A079466 A217086

Adjacent sequences: A089181 A089182 A089183 * A089185 A089186 A089187

Keyword

nonn,uned,base

Author

Roger L. Bagula, Dec 07 2003

Status

approved