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A255010 a(n) = A099795(n)^-1 mod prime(n). 3
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..63.

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 A323326

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

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Last modified November 20 12:13 EST 2019. Contains 329335 sequences. (Running on oeis4.)