login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080909 (2n+1)! modulo 4n+3. 1
1, -1, -1, 0, -1, 1, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, -1, 1, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If 4n+3 is composite, then a(n)=0. If 4n+3 is prime, then a(n)=(-1)^m where m is the number of quadratic non-residues less than or equal to 2n+1. Is there a way to predict whether a(n)=1 or a(n)=-1 ?

REFERENCES

Hardy G. H., Wright E. M., An introduction to the theory of number (fourth edition, 1960), section 7.7: the residue of ((p-1)/2)!

LINKS

Table of n, a(n) for n=0..70.

FORMULA

a(n) = mods((2*n+1)!, 4*n+3)

EXAMPLE

a(3)=0 since 7! = 0 modulo 15 and a(4)=1 since 9! = -1 modulo 19.

MAPLE

for n from 0 to 20 do mods((2*n+1)!, 4*n+3) end do;

PROG

(PARI) a(n)= {v =(2*n+1)! % (4*n+3); if (2*v > 4*n+3, v -= 4*n+3); return (v); } \\ Michel Marcus, Jul 21 2013

CROSSREFS

Sequence in context: A145361 A130304 A118274 * A087755 A050072 A156707

Adjacent sequences:  A080906 A080907 A080908 * A080910 A080911 A080912

KEYWORD

sign

AUTHOR

Christophe Leuridan (ChristopheLeuridan(AT)ujf-grenoble.fr), Apr 01 2003

EXTENSIONS

More terms from Michel Marcus, Jul 21 2013

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 00:42 EST 2017. Contains 294957 sequences.