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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322000 Nonnegative integers, sorted by increasing value of A028897(n) = Sum d[i]*2^i for n = Sum d[i]*10^i, then value of n. 4
0, 1, 2, 10, 3, 11, 4, 12, 20, 100, 5, 13, 21, 101, 6, 14, 22, 30, 102, 110, 7, 15, 23, 31, 103, 111, 8, 16, 24, 32, 40, 104, 112, 120, 200, 1000, 9, 17, 25, 33, 41, 105, 113, 121, 201, 1001, 18, 26, 34, 42, 50, 106, 114, 122, 130, 202, 210, 1002, 1010, 19, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A028897(n) is the result of using the decimal digits of n, but weighting their position as in base 2. For sake of brevity we refer to this as the b-value of n in the sequel. This idea is found on the website given in links under the name "decibinary numbers".

The b-values increment by 1 at indices (of "records") 1, 2, 4, 6, 10, 14, 20, 26, 36, ... Prefixing an initial 0, the gaps between these, equal to the number of occurrences of a given b-value (0, 1, 2, ...), are 1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 13, 13, ... = A072170(n,10). In this sequence each of (1, 2, 4, 6, 10, 13, 18, ...) is repeated twice.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Robin C. Yu, Decibinary Numbers, on Hackerrank.com.

EXAMPLE

The first terms of the sequence are as follows: (b = A028897)

  n | 0 | 1 | 2 | 10 | 3 | 11 | 4 | 12 | 20 | 100 | 5 | 13 | 21 | 101 | ...

----+---+---+---+----+---+----+---+----+----+-----+---+----+----+-----+-----

b(n)| 0 | 1 | 2 |  2 | 3 |  3 | 4 |  4 |  4 |  4  | 5 |  5 |  5 |  5  | ...

For example, b(345) = 3*2^2 + 4*2 + 5 = 25.

MAPLE

N:= 30: # for all numbers with A028897(n) <= N

L:= {seq([i, i], i=0..9)}: Agenda:= {seq([i, i], i=1..9)}:

extend:= proc(p) local x;  op(select(t -> t[2]<=N, [seq([10*p[1]+x, 2*p[2]+x], x=0..9)])); end proc:

sorter:= proc(p1, p2) if p1[2] <> p2[2] then p1[2] < p2[2] else p1[1] < p2[1] fi end proc:

while Agenda <> {} do

  Agenda:= map(extend, Agenda);

  L:= L union Agenda;

od:

L:= sort( convert(L, list), sorter):

map(t -> t[1], L); # Robert Israel, Feb 24 2019

PROG

(PARI) my(A028897(n)=fromdigits(digits(n), 2), S=[]); for(k=1, 2^10, (t=A028897(k))>9||S=setunion(S, [[t, k]])); apply(t->t[2], S)

CROSSREFS

Cf. A028897, A072170 (see comments).

Sequence in context: A317549 A239083 A239084 * A061196 A239136 A239137

Adjacent sequences:  A321997 A321998 A321999 * A322001 A322002 A322003

KEYWORD

nonn,base,look

AUTHOR

M. F. Hasler, Feb 13 2019

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)