login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A266946 Smallest number of each digital type. 3
1, 10, 11, 100, 101, 102, 110, 111, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1023, 1100, 1101, 1102, 1110, 1111, 10000, 10001, 10002, 10010, 10011, 10012, 10020, 10021, 10022, 10023, 10100, 10101, 10102, 10110, 10111, 10112, 10120, 10121, 10122, 10123, 10200, 10201, 10202, 10203, 10210, 10211, 10212, 10213, 10220, 10221, 10222, 10223, 10230, 10231, 10232, 10233, 10234, 11000, 11001, 11002, 11010, 11011, 11012, 11020, 11021, 11022, 11023, 11100, 11101, 11102, 11110, 11111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The smallest single-digit positive number is 1. This is the first type.

The smallest of the two-digit positive numbers with distinct digits is 10. This is the second type. The smallest of two-digit positive numbers with equal digits is 11. This is the third type, etc.

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..5295

FORMULA

The number of distinct types of k-digit numbers equals A164864(k).

EXAMPLE

The first 3-digit number is 100 = a(4).

The following number is 101. It does not belong to the type 100, since the first and the third digits coincide in 101, while in 100 they do not. So 101 is a new type, and a(5)=101.

Next consider 102. Here there are 3 distinct digits, so 102 is a new type, and a(6)=102. However, 103,104,105,106,107,108,109 have also 3 distinct digits, i.e. they belong to type 102.

Further, 110 belongs to neither type 100 nor type 101, since in 110 the first and the second digits coincide, while not in 100 and 101, so a(7)=110; also 111 is a new type, where all digits coincide.

Now we see that every 3-digit number is of one of the 5 types a(4),a(5),a(6),a(7),a(8).

Next we consider the first 4-digit number a(9)=1000, etc.

CROSSREFS

Cf. A164864, A264406.

Sequence in context: A136830 A153069 A178569 * A081551 A257831 A007088

Adjacent sequences:  A266943 A266944 A266945 * A266947 A266948 A266949

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev, Jan 06 2016

EXTENSIONS

More terms from Peter J. C. Moses, Jan 06 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 12:10 EST 2018. Contains 299411 sequences. (Running on oeis4.)