|
|
A216160
|
|
2^(2p-2) modulo p^3 for p=odd primes.
|
|
1
|
|
|
16, 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, 437845, 311632, 363522, 1972311, 38777, 202213, 414082, 1471674, 860550, 346186
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
2^(4*n) == (-1)^n*(2n)!/(n!)^2 (modulo p^3) (with n = (p-1)/2) for odd primes. Except for p = 3 (n = 1), where the second expression = 25 instead of 16.
|
|
LINKS
|
|
|
MAPLE
|
a:= proc(n) local p; p:= ithprime(n+1);
2 &^ (2*p-2) mod p^3
end:
|
|
MATHEMATICA
|
Table[Mod[2^(2Prime[n] - 2), Prime[n]^3], {n, 2, 30}] (* Alonso del Arte, Sep 03 2012 *)
|
|
PROG
|
(PARI) a(n) = { local(p); p = prime(n+1); return (2^(2*p-2) % (p^3)); }
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|