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

Author

Joseph L. Pe, Jan 15 2003

Keywords

• base
• nonn
• nice

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).

Examples

			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.
		

Crossrefs

Cf. A005150.

Programs

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 *)

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