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 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)
 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 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

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