A067139 Irreducible elements in OR-numbral arithmetic.

1, 2, 3, 5, 9, 11, 13, 17, 19, 23, 25, 29, 33, 35, 37, 39, 41, 43, 49, 53, 57, 65, 67, 69, 71, 75, 77, 79, 81, 83, 87, 89, 93, 97, 101, 105, 107, 113, 117, 121, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 157, 159, 161, 163, 167, 169, 171, 177, 179

Offset: 1

Author

Jens Voß, Jan 02 2002

Keywords

• nonn
• nice

Comments

Numbers m such that there is no number d in the range 1 < d < m with d*k = m for any 1 < k < m, where * is defined in A066376.

See A048888 for the definition of OR-numbral arithmetic. Note that 2 is the only prime element in OR-numbral arithmetic; for all other nonunit irreducibles x there exist numbers a and b not divisible by x such that x is a divisor of a * b.

Numbers m such that A066376(m) = 1.

1 together with primes in lunar arithmetic base 2. - N. J. A. Sloane, Aug 14 2010

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..500
• D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [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, A067138, A048888, A007059.

See A169912 for the number of elements that are n bits long - N. J. A. Sloane, Aug 31 2010. See A171000 for the binary expansions.

Programs

Haskell

import Data.List (elemIndices)
a067139 n = a067139_list !! (n-1)
a067139_list = 1 : map (+ 1) (elemIndices 1 a066376_list)
-- Reinhard Zumkeller, Mar 01 2013

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe and Joshua Zucker, Jun 12 2007