A067398 Squares in OR-numbral arithmetic.

0, 1, 4, 7, 16, 21, 28, 31, 64, 73, 84, 95, 112, 125, 124, 127, 256, 273, 292, 311, 336, 341, 380, 383, 448, 473, 500, 511, 496, 509, 508, 511, 1024, 1057, 1092, 1127, 1168, 1205, 1244, 1279, 1344, 1385, 1364, 1407, 1520, 1533, 1532, 1535, 1792, 1841, 1892

Offset: 0

Author

Jens Voß, Jan 23 2002

Keywords

• nonn

Comments

See A048888 for the definition of OR-numbral arithmetic.

Or, squares in lunar arithmetic base 2, written in base 10. - N. J. A. Sloane, Oct 02 2010

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• 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, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
• A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, J. Integer Seq., Vol. 9 (2006), Article 06.3.1.
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

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

Programs

Haskell

a067398 :: Integer -> Integer
a067398 0 = 0
a067398 n = orm n n where
   orm 1 v = v
   orm u v = orm (shiftR u 1) (shiftL v 1) .|. if odd u then v else 0
-- Reinhard Zumkeller, Mar 01 2013