|
This sequence was initially intended for (method A - initial term is 11), which is just A005150 without the first term.
[From Comments in A005150] Proof that 333 never appears in any a(n): suppose it appears for the first time in a(n); because of 'three 3' in 333, it would imply that 333 is also in a(n-1), which is a contradiction. - Jean-Christophe Hervé, May 09 2013
In fact, 333 is the smallest positive integer (ignoring leading zeros) that is only found within some term of a Look and Say sequence if it is contained in the initial term. Indeed:
For 1-digit number d, take any digit x!=d, so initial term xx...x (d times) does not contain d, but its second term dx does;
For 2-digit number cd with c!=d, use initial term dd...d (c times);
For 2-digit number cc, use initial term cxx...x (x!=c repeated c times);
For 3-digit number 1cd, use cxx...x (x!=d repeated d times);
For 3-digit number 2cd, use ccxx...x (x!=d repeated d times);
For 3-digit number 3cd<333, use cccxx...x (x!=d repeated d times).
| 