A067398 - OEIS

%I #23 Jan 28 2019 10:00:48

%S 0,1,4,7,16,21,28,31,64,73,84,95,112,125,124,127,256,273,292,311,336,

%T 341,380,383,448,473,500,511,496,509,508,511,1024,1057,1092,1127,1168,

%U 1205,1244,1279,1344,1385,1364,1407,1520,1533,1532,1535,1792,1841,1892

%N Squares in OR-numbral arithmetic.

%C See A048888 for the definition of OR-numbral arithmetic.

%C Or, squares in lunar arithmetic base 2, written in base 10. - _N. J. A. Sloane_, Oct 02 2010

%C This sequence is not multiplicative; for example a(15) = 127 != 7 * 21 = a(3) * a(5). It is totally OR-numbral multiplicative: a([n] * [m]) = [a(n)] * [a(m)] in OR-numbral arithmetic. - _Franklin T. Adams-Watters_, Oct 27 2006

%H Reinhard Zumkeller, <a href="/A067398/b067398.txt">Table of n, a(n) for n = 0..10000</a>

%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, 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 A. Frosini and S. Rinaldi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Frosini/fros2.html">On the Sequence A079500 and Its Combinatorial Interpretations</a>, J. Integer Seq., Vol. 9 (2006), Article 06.3.1.

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

%e A067398(5) = 21 since [5] * [5] = [21] in OR-numbral arithmetic.

%o (Haskell)

%o a067398 :: Integer -> Integer

%o a067398 0 = 0

%o a067398 n = orm n n where

%o    orm 1 v = v

%o    orm u v = orm (shiftR u 1) (shiftL v 1) .|. if odd u then v else 0

%o -- _Reinhard Zumkeller_, Mar 01 2013

%Y Cf. A003986, A007059, A048888, A067138, A067139, A067399, A067400, A067401.

%K nonn

%O 0,3

%A _Jens Voß_, Jan 23 2002