A113918 Cardinality of Image^inf({ 2 }) under repeated base-n zero-split squaring.

2, 18, 2, 3050, 34762, 3087549, 2

Offset: 2

Author

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

Keywords

• nonn
• hard

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.

Examples

			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.
		

Links

• Hugo van der Sanden, Perl and C implementations, Feb 03 2015

Crossrefs

Cf. A113917.

Extensions

Corrected by Hugo van der Sanden, Feb 03 2015