A089184 - OEIS

%I #10 May 15 2013 02:05:04

%S 1,22,111,4444,33333,333333,3333333,13333133,133331133,3323333233,

%T 31133331133,333343333433,3333333333333,33333333333333,

%U 333333333333333,3313333333313333,31133333333113333,333323333333323333

%N 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.

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

%t 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}]

%Y Cf. A007907.

%K nonn,uned,base

%O 2,2

%A _Roger L. Bagula_, Dec 07 2003