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

%I

%S 2,18,2,3050,34762,3087549,2

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

%C 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 }) |.

%C Conjecture: a(n) is finite for all n.

%H Hugo van der Sanden, <a href="https://github.com/hvds/seq/tree/master/zerofree">Perl and C implementations</a>, Feb 03 2015

%e f_10(29648) = { 4, 39, 879 } since 29648^2 = 879003904.

%e a(8) = 2 since Image_8({ 2 }) = { 2, 4 } and f_8({ 2, 4 }) = { 2, 4 } and |{ 2, 4 }| is 2.

%Y Cf. A113917.

%K nonn,hard

%O 2,1

%A _Hugo van der Sanden_ extending a suggestion from _David W. Wilson_, Jan 31 2006

%E Corrected by _Hugo van der Sanden_, Feb 03 2015

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Last modified October 21 05:28 EDT 2021. Contains 348141 sequences. (Running on oeis4.)