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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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." LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 EXAMPLE 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. 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 *) CROSSREFS Cf. A001651, A008585, A097488. Sequence in context: A263814 A179130 A234486 * A186198 A188155 A061660 Adjacent sequences:  A097497 A097498 A097499 * A097501 A097502 A097503 KEYWORD base,easy,nonn AUTHOR Eric Angelini, Sep 19 2004 EXTENSIONS Name, Comments, and Example edited by Danny Rorabaugh, Nov 28 2015 More terms from Michael De Vlieger, Nov 30 2015 STATUS approved

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Last modified July 17 16:58 EDT 2019. Contains 325107 sequences. (Running on oeis4.)