A068663 Let N = 23571113171923293137... the concatenation of primes; partition this number into minimal strings of composite numbers.
235, 711, 1317, 192, 32, 9, 31374, 14, 34, 75, 35, 9, 6, 16, 77, 1737, 9, 8, 38, 9, 9, 710, 110, 310, 710, 9, 1131, 27, 1311, 371, 39, 14, 9, 15, 115, 716, 316, 717, 3179, 18, 119, 119, 319, 7199, 21, 12, 232, 27, 22, 9, 2332, 39, 24, 12, 51, 25, 72, 6, 32, 6, 9, 27, 12
Offset: 1
Examples
From _Michael De Vlieger_, Nov 30 2015: (Start)
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.
Composite terms are formed such that the following term has no leading zeros, so as to preserve all the digits of N.
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.
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)
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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 *)
Extensions
Corrected and extended by Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), May 06 2002
Comments