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A097487 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.

%I A097487 #33 Nov 30 2015 18:32:31
%S A097487 235,711,1,3171,9,232,93,1374,14,34,75,35,96,16,77,1737,98,38,99,710,
%T A097487 110,310,71091,1312,713,1137,1391,4,91,51,15,716,316,717,3179,18,119,
%U A097487 11931,97199,21,12,2322,72,292,33,2392,412,512,57,26,32,6,92,712,772,8
%N A097487 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 A097487 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 A097487 Alois P. Heinz, <a href="/A097487/b097487.txt">Table of n, a(n) for n = 1..10000</a>
%H A097487 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 A097487 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 A097487 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 A097487 Cf. A068663, A097968, A098067, A098099.
%K A097487 base,easy,look,nonn
%O A097487 1,1
%A A097487 _Eric Angelini_, Sep 19 2004; corrected Sep 23 2004