A047841 -id:A047841 - cp's OEIS frontend

A103618 Number of steps required for n to reach a digit count invariant or cycle loop under the 'Look and Say' function A045918.

10, 12, 11, 12, 8, 10, 10, 10, 10, 10, 9, 11, 10, 11, 7, 9, 9, 9, 9, 9, 6, 10, 0, 9, 6, 6, 6, 6, 6, 6, 8, 11, 9, 10, 6, 8, 8, 8, 8, 8, 9, 7, 6, 6, 7, 8, 9, 9, 9, 9, 10, 9, 6, 8, 8, 7, 9, 10, 10, 10, 12, 9, 6, 8, 9, 9, 7, 10, 12, 12, 13, 9, 6, 8, 9, 10, 10, 7, 12, 13, 14, 9, 6, 8, 9, 10, 12, 12, 7, 13

Offset: 1

Lekraj Beedassy, Mar 25 2005

			a(10)=9 because we have the 9-step chain 10 -> 1011 -> 1031 -> 102113 -> 103112113 -> 10411223 -> 1031221314 -> 1041222314 -> 1031321324 -> 1031223314, the latter being autobiographical, hence invariant. Also, a(40)=9 since we have the digit count iteration 40 -> 1014 -> 102114 -> 10311214 -> 1041121314 -> 1051121324 -> 104122131415 -> 105122132415 -> 104132131425 -> 104122232415 <-> 103142132415, ending in a 2-cycle loop.

Madras Math., Descriptive Numbers: Table of results

Cf. A005151, A047841, A104785, A104786, A104787, A308781 (duplicate?).

Corrected and extended by Sean A. Irvine, Feb 08 2010

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

Original entry on oeis.org

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

Julien Kluge, Jan 31 2016

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

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

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

A005151 shows a(1) at term number 13.

Cf. A047841.

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]

A173095 Partial sums of A108810.

Original entry on oeis.org

10153331, 20326464, 30559685, 40871218, 51193539, 63296870, 75460003, 87623334, 99816467, 112128400, 124441719, 139544852, 154778073, 170089706, 185421637, 200754756, 216907889, 233061220, 249234353, 265565884, 281897715

Offset: 1

Jonathan Vos Post, Feb 09 2010

Partial sums of self-describing primes, where the digits are described in any order, whereas in A047841 they must be described in increasing order. The subsequence of prime partial sums of self-describing primes begins: 10153331, 75460003. What is the smallest value in the subsubsequence of self-describing prime partial sums of self-describing primes?

			a(7) = 10153331 + 10173133 + 10233221 + 10311533 + 10322321 + 12103331 + 12163133 = 75460003 is prime. a(21) = 10153331 + 10173133 + 10233221 + 10311533 + 10322321 + 12103331 + 12163133 + 12163331 + 12193133 + 12311933 + 12313319 + 15103133 + 15233221 + 15311633 + 15331931 + 15333119 + 16153133 + 16153331 + 16173133 + 16331531 + 16331831.

Jud McCranie, Prime Curios, Self-describing primes.

Cf. A000040, A047841, A059504, A108810, A109775, A109776.

a(n) = SUM[i=1..n] A108810(i).

cp's OEIS Frontend

A103618 Number of steps required for n to reach a digit count invariant or cycle loop under the 'Look and Say' function A045918.

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

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A173095 Partial sums of A108810.

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