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A097487
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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.
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5
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235, 711, 1, 3171, 9, 232, 93, 1374, 14, 34, 75, 35, 96, 16, 77, 1737, 98, 38, 99, 710, 110, 310, 71091, 1312, 713, 1137, 1391, 4, 91, 51, 15, 716, 316, 717, 3179, 18, 119, 11931, 97199, 21, 12, 2322, 72, 292, 33, 2392, 412, 512, 57, 26, 32, 6, 92, 712, 772, 8
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OFFSET
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1,1
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COMMENTS
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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."
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LINKS
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Eric Angelini, Jeux de suites, in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
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EXAMPLE
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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).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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