A224807 (-1)^((p-1)/2)*Binomial(p-1,(p-1)/2) mod p^3 where p is the n-th prime.

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

Offset

2,1

Comments

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)

Links

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

Maple

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)

Crossrefs

Sequence in context: A040609 A040607 A248139 * A040606 A091736 A245631

Adjacent sequences: A224804 A224805 A224806 * A224808 A224809 A224810

Keyword

nonn

Author

Gary Detlefs, Apr 18 2013

Status

approved