

A113918


Cardinality of Image^inf({ 2 }) under repeated basen zerosplit squaring.


2




OFFSET

2,1


COMMENTS

Define f_b(x) to be the set of base b numbers left after splitting x^2 at its zero digits and Image_b(S) = union_{x in S}{ { x } union f_b(S) }, then a(n) =  Image_n^inf({ 2 }) .
Conjecture: a(n) is finite for all n.


LINKS



EXAMPLE

f_10(29648) = { 4, 39, 879 } since 29648^2 = 879003904.
a(8) = 2 since Image_8({ 2 }) = { 2, 4 } and f_8({ 2, 4 }) = { 2, 4 } and { 2, 4 } is 2.


CROSSREFS



KEYWORD

nonn,hard


AUTHOR



EXTENSIONS



STATUS

approved



