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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.
5
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
OFFSET
1,1
COMMENTS
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."
LINKS
Eric Angelini, Jeux de suites, in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
EXAMPLE
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).
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[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 *)
CROSSREFS
KEYWORD
base,easy,look,nonn
AUTHOR
Eric Angelini, Sep 19 2004; corrected Sep 23 2004
STATUS
approved