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 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 Vincenzo Librandi, Table of n, a(n) for n = 1..1000 F. Morley, Note on the Congruence 2^4n == (-1)^n*(2n)!/(n!)^2 where 2n+1 is a prime, Annals of Mathematics, Vol. 9 (1894 - 1895), pp. 168-170. MAPLE a:= proc(n) local p; p:= ithprime(n+1); 2 &^ (2*p-2) mod p^3 end: seq (a(n), n=1..50); # Alois P. Heinz, Sep 05 2012 MATHEMATICA Table[Mod[2^(2Prime[n] - 2), Prime[n]^3], {n, 2, 30}] (* Alonso del Arte, Sep 03 2012 *) Table[PowerMod[2, 2p-2, p^3], {p, Prime[Range[2, 40]]}] (* Harvey P. Dale, Jun 09 2024 *) PROG (PARI) a(n) = { local(p); p = prime(n+1); return (2^(2*p-2) % (p^3)); } CROSSREFS Cf. A065091. Sequence in context: A057964 A302463 A303245 * A302371 A303087 A302892 Adjacent sequences: A216157 A216158 A216159 * A216161 A216162 A216163 KEYWORD nonn AUTHOR Michel Marcus, Sep 03 2012 STATUS approved

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Last modified August 12 03:23 EDT 2024. Contains 375085 sequences. (Running on oeis4.)