A097500 Consider the succession of single digits of A008585 (multiples of 3): 3 6 9 1 2 1 5 1 8 2 1 2 4 2 7 3 0 .... This sequence gives the lexicographically earliest derangement of A001651 (non-multiples of 3) that produces the same succession of digits.

3691, 2, 1, 5, 182, 124, 27303336394, 245, 4, 8, 515, 457, 606366697, 275, 7, 88, 184, 879093969910, 2105, 10, 811, 11, 14, 1171, 20, 1231, 26, 1291, 32, 13, 5138, 1411, 44, 1471, 50, 1531, 56, 1591, 62, 16, 5168, 17, 1174, 1771, 80, 1831, 86, 1891, 92, 19, 5198, 20120, 4207, 2102, 1321, 62192, 22

Offset: 1

Author

Eric Angelini, Sep 19 2004

Keywords

• base
• easy
• nonn

Comments

Derangement here means a(n) != A008585(n) for all n.

Original name: "Write each non-multiple of 3 integer >0 on a single label. Put the labels in numerical order to form an infinite sequence L. Now consider the succession of single digits of A008585 (multiples of 3): 3,6,9,1,2,1,5,1,8,2,1,2,4,2,7,3,0,3,3,3,6,3,9,4,2,4,5,4,8,5,1,5,4,5,7,6,0... The sequence S gives a rearrangement of the labels that reproduces the same succession of digits, subject to the constraint that the smallest label must be used that does not lead to a contradiction."

This could be roughly rephrased like this: "Rewrite in the most economical way the 'multiples-of-3 pattern' using only non-multiples of 3. Do not use any non-multiple of 3 twice."

Examples

			We must begin with "3,6,9,12,..." and we cannot represent "3" with 3, 36, or 369, because they are all multiples of 3. So the first possibility for a(1) is 3691.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001651, A008585, A097488.

Programs

Mathematica

f[lst_List, k_] := Block[{L = lst, g, a = {}, m = 0}, g[] := {Set[m, First@ FromDigits@ Append[IntegerDigits@ m, First@ #]], Set[L, Last@ #]} &@ TakeDrop[L, 1]; Do[g[]; While[Or[Mod[m, 3] == 0, First@ L == 0, MemberQ[a, m]], g[]]; AppendTo[a, m]; m = 0, {k}]; a]; f[Flatten@ Map[IntegerDigits, Array[3 # &, {120}]], 57] (* Michael De Vlieger, Nov 30 2015, Version 10.2 *)

Extensions

Name, Comments, and Example edited by Danny Rorabaugh, Nov 28 2015

More terms from Michael De Vlieger, Nov 30 2015