A268312 First number of the periodic part of the "Say what you see" trajectory (see A005151) of n.

1031223314, 21322314, 21322314, 21322314, 21322314, 3122331415, 3122331416, 3122331417, 3122331418, 3122331419, 1031223314, 21322314, 21322314, 21322314, 21322314, 3122331415, 3122331416, 3122331417, 3122331418, 3122331419, 10311233, 21322314, 22, 21322314, 31123314, 31123315

Offset

0,1

Comments

a(40) is the first time the periodic part of the trajectory contains more than one term.

Links

Julien Kluge, Table of n, a(n) for n = 0..10000

Example

Consider the starting value n = 5. We see one five: 15. We have one ones and one 5: 1115. We have three ones and one five: 3115... We reach 3122331415 which produces itself. So a(5) = 3122331415.

Mathematica

a005151[n_, m_] :=
  FromDigits[
   Reverse /@
     Sort[Tally[
       If[n == 2, m, a005151[n - 1, m]] //
        IntegerDigits], #1[[1]] < #2[[1]] &] // Flatten];
a[n_] := Block[{previousNum = 0, currentNum = 1, knownNums = {n}},
  For[i = 2, currentNum != previousNum, ++i,
   previousNum = currentNum;
   currentNum = a005151[i, n];
   If[MemberQ[knownNums, currentNum], Return[currentNum],
    AppendTo[knownNums, currentNum]];
   ];
  Return[currentNum];
  ]
a /@ Range[0, 100]

Crossrefs

A005151 shows a[1] at term number 13.

Cf. A047841.

Sequence in context: A036745 A225218 A359342 * A035124 A197952 A321066

Adjacent sequences: A268309 A268310 A268311 * A268313 A268314 A268315

Keyword

nonn,easy,base

Author

Julien Kluge, Jan 31 2016

Status

approved