VOOZH about

URL: https://oeis.org/A255010

⇱ A255010 - OEIS

login
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
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
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)];
(SageMath) [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
KEYWORD
nonn
AUTHOR
Bruno Berselli, Feb 13 2015 - proposed by Umberto Cerruti (Department of Mathematics "Giuseppe Peano", University of Turin, Italy)
STATUS
approved