A254638 Cardinality of Image^inf({ 2 }) under repeated base-n zero-split doubling.

2, 6, 2, 20, 13, 72, 3, 92, 42, 308, 34, 900, 178, 1739, 4, 3349, 443, 4523, 387, 14364, 1827, 18672, 234, 39426, 15882, 52664, 8858, 128253, 28346, 123087, 5, 259207, 87797, 363512, 44545, 671389, 182549, 1336282, 18049, 1289210, 634402, 2679419, 156629

Offset

2,1

Comments

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 }) |.

Links

Hugo van der Sanden, Table of n, a(n) for n = 2..62

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

Example

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.

Crossrefs

Cf. A254637, A113918.

Sequence in context: A257252 A327171 A008556 * A320118 A320016 A096485

Adjacent sequences: A254635 A254636 A254637 * A254639 A254640 A254641

Keyword

nonn,easy

Author

Hugo van der Sanden, Feb 03 2015

Status

approved