A268312 - OEIS

%I #18 Dec 03 2016 12:12:24

%S 1031223314,21322314,21322314,21322314,21322314,3122331415,3122331416,

%T 3122331417,3122331418,3122331419,1031223314,21322314,21322314,

%U 21322314,21322314,3122331415,3122331416,3122331417,3122331418,3122331419,10311233,21322314,22,21322314,31123314,31123315

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

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

%H Julien Kluge, <a href="/A268312/b268312.txt">Table of n, a(n) for n = 0..10000</a>

%e 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.

%t a005151[n_, m_] :=

%t   FromDigits[

%t    Reverse /@

%t      Sort[Tally[

%t        If[n == 2, m, a005151[n - 1, m]] //

%t         IntegerDigits], #1[[1]] < #2[[1]] &] // Flatten];

%t a[n_] := Block[{previousNum = 0, currentNum = 1, knownNums = {n}},

%t   For[i = 2, currentNum != previousNum, ++i,

%t    previousNum = currentNum;

%t    currentNum = a005151[i, n];

%t    If[MemberQ[knownNums, currentNum], Return[currentNum],

%t     AppendTo[knownNums, currentNum]];

%t    ];

%t   Return[currentNum];

%t   ]

%t a /@ Range[0, 100]

%Y A005151 shows a[1] at term number 13.

%Y Cf. A047841.

%K nonn,easy,base

%O 0,1

%A _Julien Kluge_, Jan 31 2016