A191701 In base-2 lunar arithmetic, number of binary numbers x of length n such that x*x has no zeros.

1, 1, 1, 1, 2, 3, 5, 9, 15, 28, 50, 95, 174, 337, 637, 1231, 2373, 4618, 8974, 17567, 34387, 67561, 132945, 262096, 517373, 1023366, 2025627, 4014861, 7964971, 15814414, 31424805, 62490481, 124330234, 247514283, 492990898, 982307460, 1958093809, 3904594162, 7788271542, 15539347702, 31012331211

Offset

1,5

Links

Table of n, a(n) for n=1..41.

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

D. Applegate, M. LeBrun, and N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.

Van Vinh Dang, Nataliya Dodonova, Mikhail Dodonov, and Svetlana Korabelshchikova, Some Applications of Binary Lunar Arithmetic, Proceedings of the VI International Conference on Information Technology and Nanotechnology, Data Science Session (ITNT-DS 2020), Vol. 2667, 75-79.

Svetlana Korabelshchikova, Some applications of binary lunar arithmetic, talk in Russian with English slides, based on previous paper.

Index entries for sequences related to dismal (or lunar) arithmetic

Formula

a(n) >= A167510(n). - Michael Chu, Oct 27 2023

Example

a(7)=5 since the following five vectors all have lunar squares equal to 1111111111111: 1101011, 1101111, 1110111, 1111011, 1111111.

Crossrefs

Sequence in context: A092424 A167510 A351359 * A066726 A124642 A370641

Adjacent sequences: A191698 A191699 A191700 * A191702 A191703 A191704

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 12 2011, corrected Jun 13 2011

Extensions

a(20) through a(41) from N. J. A. Sloane, Jun 14 2011

Status

approved