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%I #23 Jan 25 2023 13:57:18
%S 1,2,3,2,1,10,7,15,20,1,14,19,11,23,6,11,45,42,37,34,10,29,76,77,14,
%T 71,12,88,40,22,30,75,115,59,110,14,113,154,13,154,142,40,50,25,71,16,
%U 11,18,91,174,138,35,115,38,27,195,206,113,75,119,181,111,203
%N a(n) = A099795(n)^-1 mod prime(n).
%C By the definition, a(n)*A099795(n) == 1 (mod prime(n)).
%C a(n) is 1 with the primes 2, 11, 29, 787, 15773 (see A178629).
%H Robert Israel, <a href="/A255010/b255010.txt">Table of n, a(n) for n = 1..10000</a>
%H Umberto Cerruti, <a href="/A255010/a255010.pdf">Il Teorema Cinese dei Resti</a> (in Italian), 2015. The sequence is on page 21.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ModularInverse.html">Modular Inverse</a>
%F a(n) = A254939(n)/A099795(n).
%p with(numtheory): P:=proc(q) local a, n; a:=[];
%p for n from 1 to q do a:=[op(a),n]; if isprime(n+1) then print(lcm(op(a))^(-1) mod (n+1)); fi;
%p od; end: P(10^3); # _Paolo P. Lava_, Feb 16 2015
%t r[k_] := LCM @@ Range[k]; t[k_] := PowerMod[r[k - 1], -1, k]; Table[t[Prime[n]], {n, 1, 70}]
%o (Magma) [Modinv(Lcm([1..p-1]),p): p in PrimesUpTo(400)];
%o (Sage) [inverse_mod(lcm([1..p-1]),p) for p in primes(400)]
%o (PARI) a(n) = lift(1/Mod(lcm(vector(prime(n)-1, k, k)), prime(n))); \\ _Michel Marcus_, Feb 13 2015
%Y Cf. A000040, A099795, A178629, A254924, A254939.
%K nonn
%O 1,2
%A _Bruno Berselli_, Feb 13 2015 - proposed by Umberto Cerruti (Department of Mathematics "Giuseppe Peano", University of Turin, Italy)
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