A254638 - OEIS

%I #7 May 24 2024 15:54:34

%S 2,6,2,20,13,72,3,92,42,308,34,900,178,1739,4,3349,443,4523,387,14364,

%T 1827,18672,234,39426,15882,52664,8858,128253,28346,123087,5,259207,

%U 87797,363512,44545,671389,182549,1336282,18049,1289210,634402,2679419,156629

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

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

%H Hugo van der Sanden, <a href="/A254638/b254638.txt">Table of n, a(n) for n = 2..62</a>

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

%e a(8) = 3 since f_8(2) = { 4 }, f_8(4) = { 1 }, f_8(1) = { 2 } so Image_8^inf({ 2 }) = { 1, 2, 4 } and |{ 1, 2, 4 }| = 3.

%Y Cf. A254637, A113918.

%K nonn,easy

%O 2,1

%A _Hugo van der Sanden_, Feb 03 2015