A348783 Let c(i) be the number of times the digit i appears in n, for 0 <= i <= 9; then a(n) is the concatenation of c(9) c(8) ... c(1) c(0), with leading 0's omitted.

1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 11, 20, 110, 1010, 10010, 100010, 1000010, 10000010, 100000010, 1000000010, 101, 110, 200, 1100, 10100, 100100, 1000100, 10000100, 100000100, 1000000100, 1001, 1010, 1100, 2000, 11000

Offset: 0

Author

N. J. A. Sloane, Nov 14 2021

Keywords

• nonn
• base
• look

Comments

"Leading zeros" means "zeros on the left".

21 -> 110 -> 21 is the first loop, when this operation is iterated. Another is 22 -> 200 -> 102 -> 111 -> 30 -> 1001 -> 22.

Suggested by an email from Allan C. Wechsler.

The numbers 2, 3, ..., 9 cannot appear, but 1 and all k >= 10 are terms. Specifically, if the decimal digits of k > 0 are d0^c, where d is a single nonzero digit and 0^c is a string of c > 0 concatenated 0's, then k appears as a(1^(d*10**(c-1))); otherwise, if the decimal digits of k are d0^cb where d and c are as before but c >= 0 and b is a string of digits not starting with 0, then k appears as a(1^(d*10^c) 0^b). - Michael S. Branicky, Nov 14 2021

Examples

			0 -> 1
1 -> 10
2 -> 100
3 -> 1000 (one 3, zero copies of 2, 1, 0, so 1 0 0 0)
4 -> 10000
5 -> 100000
6 -> 1000000
7 -> 10000000
8 -> 100000000
9 -> 1000000000
10 -> 11
11 -> 20
12 -> 110
...
2222222222 -> 1000 (ten 2's, zero 1's, zero 0's, so 10 0 0)
...
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A100910, A348138.

Programs

Mathematica

Array[FromDigits@*RotateLeft@*Reverse@*DigitCount,35,0] (* Giorgos Kalogeropoulos, Nov 15 2021 *)

PARI

apply( {A348783(n)=if(n,eval(concat([Str(#[0|d<-n,d==i])|i<-+-[-vecmax(n=digits(n))..0]])),1)}, [0..66]) \\ M. F. Hasler, Nov 15 2021

Python

def a(n):
    s = str(n)
    return int("".join(str(s.count(d)) for d in "9876543210").lstrip("0"))
print([a(n) for n in range(35)]) # Michael S. Branicky, Nov 14 2021

Extensions

More terms from Michael S. Branicky, Nov 14 2021