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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. 0
1, 22, 111, 4444, 33333, 333333, 3333333, 13333133, 133331133, 3323333233, 31133331133, 333343333433, 3333333333333, 33333333333333, 333333333333333, 3313333333313333, 31133333333113333, 333323333333323333 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 25 00:34 EDT 2021. Contains 345445 sequences. (Running on oeis4.)