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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158930 a(n) is the smallest integer not yet in the sequence with no common base-5 digit with a(n-1). 3
1, 2, 3, 4, 5, 12, 6, 10, 8, 14, 15, 7, 18, 9, 13, 20, 11, 19, 25, 17, 21, 50, 16, 22, 26, 23, 27, 24, 28, 62, 29, 63, 30, 64, 31, 52, 33, 54, 41, 60, 34, 53, 46, 65, 49, 67, 45, 68, 100, 32, 75, 36, 78, 37, 79, 56, 90, 39, 93, 35, 94, 51, 98, 55, 99, 57, 95, 61, 103, 156, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers of A031946 or of the 4th row of A051845 do not appear in this sequence. In base-5 notation the sequence reads 1,2,3,4,10,22,11,20,13,24,30,12,33,14,...

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

The terms a(1) to a(4) are the first integers in order because they have only a single, non-common digit. a(5)=5(base10)=10(base5) does not share a digit with a(4)=4(base10)=4(base5). The numbers 6(base10)=11(base5) to 9(base10)=14(base5) are ruled out for a(6) because they share a 1 with 10(base5). The numbers 10(base10)=20(base5) and 11(base10)=21(base5) are also ruled out for a(6) because they either have a 0 or a 1 in common with a(5)=10(base5). So a(6)=12(base10)=22(base5) with no 0 or 1 is selected.

MAPLE

for S in combinat:-powerset({$0..4}) minus {{}, {$0..4}} do

  if member(0, S) then Last[S]:= 0 else Last[S]:= 1 fi od:

Next:= proc(S)

  global Last; local L, nL;

  if nops(S) = 1 then Last[S]:= Last[S]*5+S[1]; return Last[S] fi;

  Last[S]:= 1+Last[S];

  L:= convert(Last[S], base, nops(S));

  nL:= nops(L);

  if (not member(0, S)) then

   if L[-1] > 1 then

    Last[S]:= (nops(S))^nL;

    L:= [0$nL, 1];

   else nL:= nL-1

   fi

  fi;

  L:= subs({seq(i-1=S[i], i=1..nops(S))}, L);

  add(L[i]*5^(i-1), i=1..nL)

end proc:

Done:= {1}:

A[1]:= 1:

for n from 2 to 100 do

  S:= {$0..4} minus convert(convert(A[n-1], base, 5), set);

  do

    x:= Next(S);

    if not member(x, Done) then break fi

  od;

  A[n]:= x;

  Done:= Done union {x};

od:

seq(A[i], i=1..100); # Robert Israel, Jun 25 2018

CROSSREFS

Cf. A067581 (base-10), A158928 (base-3), A158929 (base-4).

Sequence in context: A190783 A136367 A014545 * A065636 A229347 A135323

Adjacent sequences:  A158927 A158928 A158929 * A158931 A158932 A158933

KEYWORD

base,easy,nonn,look

AUTHOR

R. J. Mathar, Mar 31 2009

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 September 15 16:44 EDT 2019. Contains 327078 sequences. (Running on oeis4.)