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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320624 a(n) = (A006134((prime(n)-1)/2) - Legendre(prime(n), 3))/prime(n). 1
1, 2, 4, 32, 98, 1034, 3484, 41582, 1868198, 6751460, 330246410, 4522217312, 16829506610, 235344648416, 12559206444236, 683534482499900, 2599887148071402, 144419015585768252, 2117118216002111198, 8120930597438173620 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

a(n) is always an integer.

Primes p such that p^2 divides A006134((p-1)/2) - Legendre(p, 3) are p = 103, ... What's the next?

LINKS

Table of n, a(n) for n=2..21.

FORMULA

a(2) = (binomial(0, 0) + binomial(2, 1))/3 = 3/3 = 1.

a(3) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + 1)/5 = 10/5 = 2.

a(4) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + binomial(6, 3) - 1)/7 = 28/7 = 4.

PROG

(PARI) A006134(n) = sum(k=0, n, binomial(2*k, k))

a(n) = my(p=prime(n)); (A006134((p-1)/2) - kronecker(p, 3))/p

CROSSREFS

Cf. A006134, A102283, A320626.

Sequence in context: A197099 A009098 A192387 * A133127 A122693 A019060

Adjacent sequences:  A320621 A320622 A320623 * A320625 A320626 A320627

KEYWORD

nonn

AUTHOR

Jianing Song, Oct 18 2018

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 20:12 EDT 2019. Contains 327247 sequences. (Running on oeis4.)