A351653 a(n) is the concatenation of the length of each run of digits in the decimal representation of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11

Offset: 0

Author

Eder Vanzei, Feb 16 2022

Keywords

• base
• easy
• nonn

Examples

			a(100) = 12, because the 1st run (1) has length 1 and the 2nd run (00) has length 2.
a(13211) = 1112, because the 1st run (1) has length 1, the 2nd run (3) has length 1, the 3rd run (2) has length 1 and the 4th run (11) has length 2.
		

Crossrefs

Cf. A001462, A318921, A318927 (binary version).

Programs

Mathematica

a[n_] := FromDigits[IntegerDigits[Length /@ Split[IntegerDigits[n]]] // Flatten]; Array[a, 100, 0] (* Amiram Eldar, Feb 16 2022 *)

PARI

a(n) = {my(result = "", count = 0, dig = digits(n), last = dig[1]); for(i = 1, length(dig), current = dig[i]; if (current == last, count++, result = concat(result, Str(count)); count = 1); last = current); result = concat(result, Str(count)); return(eval(result))};

PARI

apply( {A351653(n,d=digits(n+!n))=d=concat([0,[k|k<-[1..#n=d[^1]-d[^-1]], n[k]], #d]); fromdigits(d[^1]-d[^-1])}, [0..77]) \\ M. F. Hasler, Aug 21 2025

Python

from itertools import groupby
def A351653(n): return int(''.join(str(len(list(g))) for k, g in groupby(str(n)))) # Chai Wah Wu, Mar 11 2022