A216208 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).

11, 121, 13231, 143424341, 15453545254535451, 165646563656465626564656365646561, 17675767476757673767576747675767276757674767576737675767476757671

Offset

1,1

Comments

Definition of "entry": Call each digit of a(1) and each inserted sum an entry.

(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).

References

S. Bobzien, Higher-order vagueness and borderline nestings - a persistent confusion, Analytic Philosophy 54 (2013), 1-49.

M. Salson, Structures d'indexation compressées et dynamiques pour le texte (doctoral dissertation, bioinformatics) Université de Rouen 2010.

Links

Table of n, a(n) for n=1..7.

Formula

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).

Example

a(2) = 121; for a(3), in 1-2-1 the two (-) are replaced by 1+2 = 3 hence a(3) = 13231.

Mathematica

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 *)

Crossrefs

Sequence in context: A080486 A342233 A082776 * A110398 A176595 A067218

Adjacent sequences: A216205 A216206 A216207 * A216209 A216210 A216211

Keyword

base,easy,nonn

Author

Susanne Bobzien, Mar 12 2013

Status

approved