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In base-2 lunar arithmetic, number of binary numbers x of length n such that x*x has no zeros.
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%I #51 Nov 22 2023 22:14:08

%S 1,1,1,1,2,3,5,9,15,28,50,95,174,337,637,1231,2373,4618,8974,17567,

%T 34387,67561,132945,262096,517373,1023366,2025627,4014861,7964971,

%U 15814414,31424805,62490481,124330234,247514283,492990898,982307460,1958093809,3904594162,7788271542,15539347702,31012331211

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

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

%H D. Applegate, M. LeBrun, and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.

%H Van Vinh Dang, Nataliya Dodonova, Mikhail Dodonov, and Svetlana Korabelshchikova, <a href="http://ceur-ws.org/Vol-2667/paper18.pdf">Some Applications of Binary Lunar Arithmetic</a>, Proceedings of the VI International Conference on Information Technology and Nanotechnology, Data Science Session (ITNT-DS 2020), Vol. 2667, 75-79.

%H Svetlana Korabelshchikova, <a href="https://www.youtube.com/watch?v=x3LPRQgd2mk">Some applications of binary lunar arithmetic</a>, talk in Russian with English slides, based on previous paper.

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

%F a(n) >= A167510(n). - _Michael Chu_, Oct 27 2023

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

%K nonn,base

%O 1,5

%A _N. J. A. Sloane_, Jun 12 2011, corrected Jun 13 2011

%E a(20) through a(41) from _N. J. A. Sloane_, Jun 14 2011