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A298208 a(n) is the smallest positive integer not yet in the sequence that shares a digit with a(n-2) and shares no digit with a(n-1); a(1) = 0, a(2) = 1. 1
0, 1, 20, 11, 2, 10, 22, 13, 24, 3, 4, 23, 14, 25, 16, 5, 6, 15, 26, 17, 28, 7, 8, 27, 18, 29, 31, 9, 12, 39, 21, 30, 19, 32, 41, 33, 40, 35, 42, 36, 44, 37, 45, 38, 46, 53, 47, 50, 34, 51, 43, 52, 48, 55, 49, 56, 74, 58, 64, 57, 60, 54, 61, 59, 62, 75, 63, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Initial fixed points are 47, 52, 56, 58, 72, 81, 94, 101, 13661, 13663. - Corrected and extended by Robert Israel, Feb 09 2018

Inverse: 0, 1, 4, 9, 10, 15, 16, 21, 22, 27, 5, 3, 28, 7, 12, 17, 14, 19, 24, 32, 2, 30, 6, 11, 8, 13, 18, 23, 20, 25, 31, ..., . - Robert G. Wilson v, Feb 09 2018

LINKS

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

MAPLE

N:= 1000: # to get all terms before the first term > N

a[1] := 0: a[2] := 1: first := 2:

Next := Array(2 .. N, i -> i+1):

Prev := Array(2 .. N, i -> i-1): Prev[2] := 0:

for n from 0 to N do

  digs[n] := convert(convert(n, base, 10), set)

od:

for n from 3 do

  D1 := digs[a[n-1]];

  D2 := digs[a[n-2]];

  t := first;

  while digs[t] intersect D2 = {} or digs[t] intersect D1 <> {} do

    t := Next[t];

    if t > N then break fi

  od;

  if t > N then break fi;

  a[n] := t;

  if Prev[t] = 0 then first := Next[t] else Next[Prev[t]] := Next[t] fi; if Next[t] <= N then Prev[Next[t]] := Prev[t] fi

od:

seq(a[i], i=1..n-1); # Robert Israel, Feb 09 2018

MATHEMATICA

f[s_List] := Block[{a = Union@ IntegerDigits@ s[[-2]], b = Union@ IntegerDigits@ s[[-1]], k = 2}, While[id = Union@ IntegerDigits@ k; MemberQ[s, k] || Intersection[a, id] == {} || Intersection[b, id] != {}, k++]; Append[s, k]]; Nest[f, {0, 1}, 66] (* Robert G. Wilson v, Feb 09 2018 *)

CROSSREFS

Cf. A107353 (where each term must share a digit with the preceding term).

Cf. A297418.

Sequence in context: A033340 A040383 A058282 * A247337 A071160 A071153

Adjacent sequences:  A298205 A298206 A298207 * A298209 A298210 A298211

KEYWORD

nonn,base,look

AUTHOR

Enrique Navarrete, Jan 15 2018

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)