A158081 Look and Say sequence: describe the previous term! (method A - initial term is 333).

333, 33, 23, 1213, 11121113, 31123113, 132112132113, 11131221121113122113, 311311222112311311222113, 1321132132211213211321322113, 11131221131211132221121113122113121113222113, 3113112221131112311332211231131122211311123113322113, 132113213221133112132123222112132113213221133112132123222113

Offset

1,1

Comments

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).

References

Marcus Du Sautoy, Symmetry: A Journey into the Patterns of Nature, Harper (March 11, 2008), p. 96.- Roger L. Bagula, Mar 12 2009

(For other references, cf. A005150.)

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..23

(For other links, cf. A005150.)

Prog

(For Look and Say code, cf. A005150.)

Crossrefs

Cf. A005150.

Sequence in context: A235020 A111690 A095199 * A248062 A056089 A227228

Adjacent sequences: A158078 A158079 A158080 * A158082 A158083 A158084

Keyword

nonn

Author

Danny Rorabaugh, Apr 01 2015

Status

approved