This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A067139 #37 Oct 08 2023 03:39:07 %S A067139 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 A067139 71,75,77,79,81,83,87,89,93,97,101,105,107,113,117,121,129,131,133, %U A067139 135,137,139,141,143,145,147,149,151,157,159,161,163,167,169,171,177,179 %N A067139 Irreducible elements in OR-numbral arithmetic. %C A067139 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 A067139 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 A067139 Numbers m such that A066376(m) = 1. %C A067139 1 together with primes in lunar arithmetic base 2. - _N. J. A. Sloane_, Aug 14 2010 %H A067139 Reinhard Zumkeller, <a href="/A067139/b067139.txt">Table of n, a(n) for n = 1..500</a> %H A067139 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 A067139 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 A067139 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 A067139 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a> %o A067139 (Haskell) %o A067139 import Data.List (elemIndices) %o A067139 a067139 n = a067139_list !! (n-1) %o A067139 a067139_list = 1 : map (+ 1) (elemIndices 1 a066376_list) %o A067139 -- _Reinhard Zumkeller_, Mar 01 2013 %Y A067139 Cf. A003986, A067138, A048888, A007059. %Y A067139 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 A067139 nonn,nice %O A067139 1,2 %A A067139 _Jens Voß_, Jan 02 2002 %E A067139 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_ and _Joshua Zucker_, Jun 12 2007