The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047845 a(n) = (m-1)/2, where m is the n-th odd nonprime (A014076(n)). 31
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 k for which A073610(2k+3)=0; values of k for which A061358(2k+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^f(3)*5^f(5)*7^f(7)*11^f(11)... . Then f(3)/f(5) = 2, f(3)/f(7) = 3, f(3)/f(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
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 k such that (2*k)!/(2*k + 1) is an integer. - Peter Bala, Jan 24 2017
Except for a(1)=0: numbers of the form k == j (mod 2j+1), j >= 1, k > 2j+1. - Bob Selcoe, Nov 07 2017
LINKS
Slate, Article about USA flag patterns -- this is where Skip Garibaldi gave definitions.
FORMULA
A193773(a(n)) > 1 for n > 1. - Reinhard Zumkeller, Jan 02 2013
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
(Magma) [(n-1)/2 : n in [1..350] | (n mod 2) eq 1 and not IsPrime(n)]; // G. C. Greubel, Oct 16 2023
(SageMath) [(n-1)/2 for n in (1..350) if n%2==1 and not is_prime(n)] # G. C. Greubel, Oct 16 2023
(PARI) print1(0, ", ");
forcomposite(n=1, 250, if(1==n%2, print1((n-1)/2, ", "))); \\ Joerg Arndt, Oct 16 2023
CROSSREFS
Complement of A005097.
Sequence in context: A025357 A222949 A144020 * A097703 A310674 A104036
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Name edited by Jon E. Schoenfield, Oct 16 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 06:59 EDT 2024. Contains 373492 sequences. (Running on oeis4.)