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%I #26 Mar 21 2013 12:23:57
%S 11,121,13231,143424341,15453545254535451,
%T 165646563656465626564656365646561,
%U 17675767476757673767576747675767276757674767576737675767476757671
%N a(1) = 11. a(n) is obtained by filling the space between neighboring entries by the sum of the first two entries of a(n-1).
%C Definition of "entry": Call each digit of a(1) and each inserted sum an entry.
%C (1) Philosophy. Sequence expresses the nesting pattern of hierarchical higher-order vagueness (formal description in Bobzien 2013, 17-20; informal description e.g. in Shapiro 2005, 147-8) (2) Biology. At least the first five numbers of the sequence are manifested in various biological structures, so in vessel arrangement in Microcosmus helleri; in the pereional appendages of Augustidontus seriatus, in the rip structure (“Berippung”) of pecten (velopecten) Vewzprimiensis Bittn.(formal description in Salson 2010, 115).
%D S. Bobzien, Higher-order vagueness and borderline nestings - a persistent confusion, Analytic Philosophy 54 (2013), 1-49.
%D M. Salson, Structures d'indexation compressées et dynamiques pour le texte (doctoral dissertation, bioinformatics) Université de Rouen 2010.
%F a(1) = 11. a(n) is obtained by filling the space between neighboring entries by the sum of the first two entries of a(n-1).
%e a(2) = 121; for a(3), in 1-2-1 the two (-) are replaced by 1+2 = 3 hence a(3) = 13231.
%t a[1]="11"; a[n_] := a[n] = StringInsert[a[n-1], ToString@n, 1 + Range[2^(n-1)]]; Table[a[n], {n, 9}] (* _Giovanni Resta_, Mar 12 2013 *)
%K base,easy,nonn
%O 1,1
%A _Susanne Bobzien_, Mar 12 2013
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