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%I #14 Nov 30 2015 19:57:51
%S 235,711,1317,192,32,9,31374,14,34,75,35,9,6,16,77,1737,9,8,38,9,9,
%T 710,110,310,710,9,1131,27,1311,371,39,14,9,15,115,716,316,717,3179,
%U 18,119,119,319,7199,21,12,232,27,22,9,2332,39,24,12,51,25,72,6,32,6,9,27,12
%N Let N = 23571113171923293137... the concatenation of primes; partition this number into minimal strings of composite numbers.
%C This could be roughly rephrased like this: "Rewrite in the most economical way the prime number 'pattern' using only composite numbers." - _Michael De Vlieger_, Nov 30 2015, after _Danny Rorabaugh_ at A097487.
%H Michael De Vlieger, <a href="/A068663/b068663.txt">Table of n, a(n) for n = 1..10000</a>
%e From _Michael De Vlieger_, Nov 30 2015: (Start)
%e We begin with N = 235711131719..., taking first digits until we have a composite concatenation. Since 2 and 23 are prime, 235 is the first term. We continue with 711131719... and since 7 and 71 are prime, 711 is the next term.
%e Composite terms are formed such that the following term has no leading zeros, so as to preserve all the digits of N.
%e The terms {710, 110, 310, 710} derive from the primes {97, 101, 103, 107, 109} and happen to be formed because eliding the zero would result in a prime in these cases.
%e a(70) = 330 because although 33 would suffice as it is composite, the zero leading next digits 07311313... would result in a(71) losing a digit of N. (End)
%t lim = 123; 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[! CompositeQ@ m, First@ L == 0], g[]]; AppendTo[a, m]; m = 0, {k}]; a]; f[Flatten@ Map[IntegerDigits, Prime@ Range@ lim], Floor[lim/2]] (* _Michael De Vlieger_, Nov 30 2015, Version 10.2 *)
%Y Cf. A000040, A033308, A097487, A098103.
%K base,nonn,look
%O 1,1
%A _Amarnath Murthy_, Mar 01 2002
%E Corrected and extended by Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), May 06 2002
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