A079475 Number described by n using the "Look and Say" rule.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 0, 111, 222, 333, 444, 555, 666, 777, 888, 999, 0, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 0

Offset

0,3

Comments

n is read one digit at a time, leftover single digits describe themselves and trailing zeros are ignored.

In many, but not all cases, a(n) acts as an inverse to the "Look and Say" sequence A005150. For example, 4113 -> 142113 under the "Look and Say" and 142113 -> 4113 under a(n).

Links

Table of n, a(n) for n=0..50.

Example

142113 can be read as one "4", two "1"s, one "3" and so describes 4113. Hence a(142113) = 4113. 123 can be read as one "2", "3" and so describes 23. (The leftover digit 3 describes itself.) Hence a(123) = 23. Note that a(1213) = 23 also. 40 can be read as four "0"s, so a(40) = 0. (Trailing zeros are ignored.) 4. a(5) = 5. A single digit describes itself.

Mathematica

a[n_] := Table[#[[2]], {#[[1]]}]& /@ Partition[If[EvenQ[Length[id = IntegerDigits[n]]], id, Join[Most[id], {1}, {id[[-1]]}]], 2] // Flatten // FromDigits; Table[a[n], {n, 0, 123}] (* Jean-François Alcover, Mar 02 2017 *)

Prog

(Python)
def A079475(n):
    s = str(n)
    l = len(s)
    if l % 2:
        s = s[:-1]+'1'+s[-1]
    return int(''.join(s[i+1]*int(s[i]) for i in range(0, l, 2))) # Chai Wah Wu, Sep 01 2021

Crossrefs

Cf. A005150.

Sequence in context: A128212 A187844 A007954 * A373102 A081286 A080867

Adjacent sequences: A079472 A079473 A079474 * A079476 A079477 A079478

Keyword

base,nonn,nice

Author

Joseph L. Pe, Jan 15 2003

Status

approved