A255010 a(n) = A099795(n)^-1 mod prime(n).

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, 71, 12, 88, 40, 22, 30, 75, 115, 59, 110, 14, 113, 154, 13, 154, 142, 40, 50, 25, 71, 16, 11, 18, 91, 174, 138, 35, 115, 38, 27, 195, 206, 113, 75, 119, 181, 111, 203

Offset

1,2

Comments

By the definition, a(n)*A099795(n) == 1 (mod prime(n)).

a(n) is 1 with the primes 2, 11, 29, 787, 15773 (see A178629).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Umberto Cerruti, Il Teorema Cinese dei Resti (in Italian), 2015. The sequence is on page 21.

Eric Weisstein's World of Mathematics, Modular Inverse

Formula

a(n) = A254939(n)/A099795(n).

Maple

with(numtheory): P:=proc(q)  local a, n;  a:=[];
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;
od; end: P(10^3); # Paolo P. Lava, Feb 16 2015

Mathematica

r[k_] := LCM @@ Range[k]; t[k_] := PowerMod[r[k - 1], -1, k]; Table[t[Prime[n]], {n, 1, 70}]

Prog

(Magma) [Modinv(Lcm([1..p-1]), p): p in PrimesUpTo(400)];
(Sage) [inverse_mod(lcm([1..p-1]), p) for p in primes(400)]
(PARI) a(n) = lift(1/Mod(lcm(vector(prime(n)-1, k, k)), prime(n))); \\ Michel Marcus, Feb 13 2015

Crossrefs

Cf. A000040, A099795, A178629, A254924, A254939.

Sequence in context: A020858 A090664 A086764 * A292371 A216683 A367896

Adjacent sequences: A255007 A255008 A255009 * A255011 A255012 A255013

Keyword

nonn

Author

Bruno Berselli, Feb 13 2015 - proposed by Umberto Cerruti (Department of Mathematics "Giuseppe Peano", University of Turin, Italy)

Status

approved