OFFSET
1,2
COMMENTS
If u, v are positive integers with gcd(u,v) = 1, the "reduced inverse" red_inv(u,v) of u mod v is u^(-1) mod v if u^(-1) mod v <= v/2, otherwise it is v - u^(-1) mod v.
That is, we map u to whichever of +-u has a representative mod v in the range 0 to v/2. Stated another way, red_inv(u,v) is a number r in the range 0 to v/2 such that r*u == +-1 mod v.
For example, red_inv(3,11) = 4, since 3^(-1) mod 11 = 4. But red_inv(2,11) = 5 = 11-6, since red_inv(2,11) = 6.
Arises in the study of A344005.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..5050 [First 100 rows, flattened]
EXAMPLE
Triangle begins:
0,
5, 0,
9, 11, 0,
13, 13, 29, 0,
21, 23, 21, 43, 0,
25, 25, 51, 27, 131, 0,
33, 35, 69, 69, 67, 103, 0,
37, 37, 39, 113, 153, 77, 305, 0,
45, 47, 91, 139, 45, 183, 137, 229, 0,
57, 59, 59, 57, 175, 233, 407, 115, 231, 0,
...
MAPLE
myfun1 := proc(A, B) local Ar, Br;
if igcd(A, B) > 1 then return(0); fi;
Ar:=(A)^(-1) mod B;
if 2*Ar > B then Ar:=B-Ar; fi;
Br:=(B)^(-1) mod A;
if 2*Br > A then Br:=A-Br; fi;
A*Ar+B*Br;
end;
myfun2:=(i, j)->myfun1(ithprime(i), ithprime(j));
for i from 1 to 20 do lprint([seq(myfun2(i, j), j=1..i)]); od:
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Sep 18 2021
STATUS
approved