

A047845


(n1)/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
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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 threedimensional 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^21)/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

Enoch Haga


STATUS

approved



