

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

Table of n, a(n) for n=2..8.
Hugo van der Sanden, Perl and C implementations, Feb 03 2015


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

Cf. A113917.
Sequence in context: A279883 A266166 A077452 * A253603 A094048 A179073
Adjacent sequences: A113915 A113916 A113917 * A113919 A113920 A113921


KEYWORD

nonn,hard


AUTHOR

Hugo van der Sanden extending a suggestion from David W. Wilson, Jan 31 2006


EXTENSIONS

Corrected by Hugo van der Sanden, Feb 03 2015


STATUS

approved



