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A107353 a(0)=0, a(n) = smallest integer not previously used which contains a digit from a(n-1). 25
0, 10, 1, 11, 12, 2, 20, 21, 13, 3, 23, 22, 24, 4, 14, 15, 5, 25, 26, 6, 16, 17, 7, 27, 28, 8, 18, 19, 9, 29, 32, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..71.

FORMULA

For n > 28, and 2 <= j <= 10, a(j*10^k) = j*10^k + (j-1).

EXAMPLE

[10] is the smallest available integer having a "0". [1] is the smallest available integer having a "1" or a "0". [11] is the smallest integer having a 1, etc.

When restricted to {0..9999} this sequence is a permutation with the following cycle representation:

(1, 10, 23, 27, 19, 6, 20, 16, 5, 2)

(3, 11, 22, 7, 21, 17, 25, 8, 13, 4, 12, 24, 28, 9)

(18, 26)

(30, 32, 31)

(40, 43, 42, 41)

(50, 54, 53, 52, 51)

(60, 65, 64, 63, 62, 61)

(70, 76, 75, 74, 73, 72, 71)

(80, 87, 86, 85, 84, 83, 82, 81)

(100, 109, 108, 107, 106, 105, 104, 103, 102, 101)

(200, 201)

(300, 302, 301)

(400, 403, 402, 401)

(500, 504, 503, 502, 501)

(600, 605, 604, 603, 602, 601)

(700, 706, 705, 704, 703, 702, 701)

(800, 807, 806, 805, 804, 803, 802, 801)

(1000, 1009, 1008, 1007, 1006, 1005, 1004, 1003, 1002, 1001)

(2000, 2001)

(3000, 3002, 3001)

(4000, 4003, 4002, 4001)

(5000, 5004, 5003, 5002, 5001)

(6000, 6005, 6004, 6003, 6002, 6001)

(7000, 7006, 7005, 7004, 7003, 7002, 7001)

(8000, 8007, 8006, 8005, 8004, 8003, 8002, 8001)

- Jason Kimberley, Dec 22 2011

MATHEMATICA

f[l_] := Block[{c = 0}, While[ MemberQ[l, c] || Intersection @@ IntegerDigits /@ {Last[l], c} == {}, c++ ]; Return[Append[l, c]] ]; Nest[f, {0}, 71] (* Ray Chandler, May 23 2005 *)

CROSSREFS

Sequence in context: A107408 A129888 A239113 * A172171 A164899 A164844

Adjacent sequences:  A107350 A107351 A107352 * A107354 A107355 A107356

KEYWORD

base,easy,nonn

AUTHOR

Eric Angelini, May 21 2005

EXTENSIONS

Extended by Ray Chandler, May 23 2005

STATUS

approved

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Last modified November 21 16:08 EST 2017. Contains 295003 sequences.