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%I #37 Oct 08 2023 03:39:07
%S 1,2,3,5,9,11,13,17,19,23,25,29,33,35,37,39,41,43,49,53,57,65,67,69,
%T 71,75,77,79,81,83,87,89,93,97,101,105,107,113,117,121,129,131,133,
%U 135,137,139,141,143,145,147,149,151,157,159,161,163,167,169,171,177,179
%N Irreducible elements in OR-numbral arithmetic.
%C 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.
%C 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.
%C Numbers m such that A066376(m) = 1.
%C 1 together with primes in lunar arithmetic base 2. - _N. J. A. Sloane_, Aug 14 2010
%H Reinhard Zumkeller, <a href="/A067139/b067139.txt">Table of n, a(n) for n = 1..500</a>
%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a>, 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]
%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="http://www.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>
%o (Haskell)
%o import Data.List (elemIndices)
%o a067139 n = a067139_list !! (n-1)
%o a067139_list = 1 : map (+ 1) (elemIndices 1 a066376_list)
%o -- _Reinhard Zumkeller_, Mar 01 2013
%Y Cf. A003986, A067138, A048888, A007059.
%Y 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.
%K nonn,nice
%O 1,2
%A _Jens Voß_, Jan 02 2002
%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_ and _Joshua Zucker_, Jun 12 2007
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