The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A224807 (-1)^((p-1)/2)*Binomial(p-1,(p-1)/2) mod p^3 where p is the n-th prime. 0
25, 6, 323, 1079, 924, 3044, 6252, 254, 21084, 4217, 42514, 48955, 63168, 101333, 90896, 87970, 164396, 100099, 85982, 221337, 464837, 90637, 214936, 735552, 171600, 330425, 437835, 311632, 363522 (list; graph; refs; listen; history; text; internal format)



This sequence is related to Morley's Congruence which states that, for prime p>2, (-1)^((p-1)/2)*binomial(p-1,(p-1)/2) == 4^(p-1) (mod p^3).

It of interest to note that this congruence can only be illustrated in Maple by using the right hand side of the identity  a== b  (mod m) iff m|(a-b). Checking for values of n^3 that divide ((-1)^((n-1)/2)*binomial(n-1,(n-1)/2) - 4^(n-1)) produces the sequence of primes. Encoding the left hand side produces this sequence.

a(n) == 1  (mod p)


Table of n, a(n) for n=2..30.


p:= n-> ithprime(n): seq((-1)^((p(n)-1)/2)*binomial(p(n)-1, (p(n)-1)/2) mod p(n)^3, n=2..30)


Sequence in context: A040609 A040607 A248139 * A040606 A091736 A245631

Adjacent sequences:  A224804 A224805 A224806 * A224808 A224809 A224810




Gary Detlefs, Apr 18 2013



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 November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)