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

0,2

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

Links

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

Example

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)
...

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A100910, A348138.

Sequence in context: A100061 A125858 A086067 * A260522 A260521 A136873

Adjacent sequences: A348780 A348781 A348782 * A348784 A348785 A348786

Keyword

nonn,base,look

Author

N. J. A. Sloane, Nov 14 2021

Extensions

More terms from Michael S. Branicky, Nov 14 2021

Status

approved