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%I #33 Nov 30 2015 18:32:31
%S 235,711,1,3171,9,232,93,1374,14,34,75,35,96,16,77,1737,98,38,99,710,
%T 110,310,71091,1312,713,1137,1391,4,91,51,15,716,316,717,3179,18,119,
%U 11931,97199,21,12,2322,72,292,33,2392,412,512,57,26,32,6,92,712,772,8
%N Write the nonprime positive integers on labels in numerical order, forming an infinite sequence L. Now consider the succession of single digits of A000040 (prime numbers): 2 3 5 7 1 1 1 3 1 7 1 9 2 3 2 9 3 1 3 7 4 1 4 3 4 7 5 3 ... (A033308). This sequence gives an arrangement L that produces the same succession of digits, subject to the constraint that the smallest unused label must be used that does not lead to a contradiction.
%C This could be roughly rephrased like this: "Rewrite in the most economical way the prime numbers 'pattern' using only nonprime numbers. Do not use any nonprime twice."
%H Alois P. Heinz, <a href="/A097487/b097487.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Angelini, <a href="http://www.pourlascience.fr/ewb_pages/a/article-jeux-de-suites-19006.php">Jeux de suites</a>, in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
%e We must begin with 2,3,5,7,11,13,... and we cannot represent "2" with the label "2" or "23", so the next possibility is the label "235" (first available nonprime number in L).
%t 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[PrimeQ@ m, MemberQ[a, m]], g[]]; AppendTo[a, m]; m = 0, {k}]; a]; f[Flatten@ Map[IntegerDigits, Prime@ Range@ 200], 56] (* _Michael De Vlieger_, Nov 29 2015, Version 10.2 *)
%Y Cf. A068663, A097968, A098067, A098099.
%K base,easy,look,nonn
%O 1,1
%A _Eric Angelini_, Sep 19 2004; corrected Sep 23 2004
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