%I A098099
%S A098099 1357911131517192,12,32,52,72,931333537394,14,34,54,74,951535557596,16,
%T A098099 36,56,76,971737577798,18,38,58,78,9919395979910,110,310,510,710,
%U A098099 911111311511711912,112,312,512,712,913113313513713914,114,314,514,714
%N A098099 Write each even integer >0 on a single label. Put the labels in numerical 
               order to form an infinite sequence L. Now consider the succession 
               of single digits of A005408 (odd numbers): 1 3 5 7 9 1 1 1 3 1 5 
               1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9... The sequence S 
               gives a rearrangement of the labels that reproduces the same succession 
               of digits, subject to the constraint that the smallest label must 
               be used that does not lead to a contradiction.
%C A098099 This could be roughly rephrased like this: "Re-write in the most economical 
               way the "odd numbers pattern" using only even numbers, but re-arranged. 
               All the numbers of the sequence must be different one from another.
%D A098099 E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, 
               Volume 59 (Jeux math'), April/June 2008, Paris.
%e A098099 We must begin with 1,3,5... and we cannot represent "1" or "13" or "135" 
               by any even label because they just do not exist (available labels 
               carry only odd numbers), so the next possibility is the label "1357911131517192". 
               For "199,201,203..." we won't be allowed to use "1992", for instance, 
               since no label begins with a 0. Labels of L cannot be used more than 
               once.
%Y A098099 Cf. A097968, A097487.
%Y A098099 Sequence in context: A095431 A072719 A134692 this_sequence A067495 A047698 
               A058445
%Y A098099 Adjacent sequences: A098096 A098097 A098098 this_sequence A098100 A098101 
               A098102
%K A098099 base,easy,nonn
%O A098099 1,1
%A A098099 Eric Angelini (eric.angelini(AT)kntv.be), Sep 22 2004