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 A047845 (n-1)/2, where n runs through odd nonprimes (A014076). 27
 0, 4, 7, 10, 12, 13, 16, 17, 19, 22, 24, 25, 27, 28, 31, 32, 34, 37, 38, 40, 42, 43, 45, 46, 47, 49, 52, 55, 57, 58, 59, 60, 61, 62, 64, 66, 67, 70, 71, 72, 73, 76, 77, 79, 80, 82, 84, 85, 87, 88, 91, 92, 93, 94, 97, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 112, 115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also (starting with 2nd term) numbers of the form 2xy+x+y for x and y positive integers. This is also the numbers of sticks needed to construct a two dimensional rectangular lattice of unit squares. See A090767 for the three-dimensional generalization. - John H. Mason, Feb 02 2004 Note that if k is not in this sequence, then 2*k+1 is prime. - Jose Brox (tautocrona(AT)terra.es), Dec 29 2005 Values of n for which A073610(2n+3)=0; Values of n for which A061358(2n+3)=0; - Graeme McRae, Jul 18 2006 This sequence also arises in the following way: take the product of initial odd numbers i.e. the product (2n+1)!/(n!2^n) and factor it into prime numbers. The result will be of the form 3^n(3)5^n(5)7^n(7)11^n(11).... . Then n(3)/n(5) = 2, n(3)/n(7) = 3,n(3)/n(11) = 5,... and this sequence forms (for sufficiently large n, of course) the sequence of natural numbers without 4,7,10,12,... i.e. these numbers are what is lacking in the present sequence. - Andrzej Staruszkiewicz (uszkiewicz(AT)poczta.onet.pl), Nov 10 2007 Let p odd prime, number in sequence, n=(p^2-1)/2 (4,12,24,60,84,...). [Vincenzo Librandi, Aug 06 2010] A193773(a(n)) > 1 for n > 1. - Reinhard Zumkeller, Jan 02 2013 Also "flag short numbers", i.e., number of dots that can be arranged in successive rows of K, K+1, K, K+1, K, ..., K+1, K (assuming there is a total of L > 1 rows of size K > 0). Adapting Skip Garibaldi's terms, sequence A053726 would be "flag long numbers" because those patterns begin and end with the long lines. If you convert dots to sticks, you get the lattice that John H. Mason mentioned. - Juhani Heino, Oct 11 2014 Numbers n such that (2*n)!/(2*n + 1) is an integer. - Peter Bala, Jan 24 2017 Except a(1)=0: numbers of the form k == j mod 2j+1, j >= 1, k > 2j+1. - Bob Selcoe, Nov 07 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Slate, Article about USA flag patterns - this is where Skip Garibaldi gave definitions MAPLE for n from 0 to 120 do     if irem(factorial(2*n), 2*n+1) = 0 then print(n); end if; end do: # Peter Bala, Jan 24 2017 MATHEMATICA (Select[Range[1, 231, 2], PrimeOmega[#] != 1 &] - 1)/2 (* Jayanta Basu, Aug 11 2013 *) PROG (Haskell) a047845 = (`div` 2) . a014076  -- Reinhard Zumkeller, Jan 02 2013 CROSSREFS Complement of A005097. Sequence in context: A025357 A222949 A144020 * A097703 A310674 A104036 Adjacent sequences:  A047842 A047843 A047844 * A047846 A047847 A047848 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified June 19 17:16 EDT 2019. Contains 324222 sequences. (Running on oeis4.)