A385050 a(n) is the least positive number k such that n is the greatest m such that k is a quadratic residue mod prime(i) for i=1..m and {k mod prime(i): i=1..m} are all distinct.

1, 3, 4, 184, 9, 1479, 20799, 31509, 162094, 83554, 828844, 895449, 4631104, 86925309, 97476129, 14684224, 33547264, 5381151099, 516743824, 1958770564, 112746608529, 3046156864, 373079083204, 1394424964, 297469886464, 1596601563489, 976001733184, 33344131402059

Offset

1,2

Comments

For n >= 4, {a(n) mod 105} = {9, 79}.

Links

Table of n, a(n) for n=1..28.

Example

a(1) = 1: |{1}| = 1: 1 mod 2 = 1^2 mod 2, terminates at 1 mod 3 (not distinct: repeats 1 mod 2).
a(2) = 3: |{1, 0}| = 2: 3 mod 2 = 1^2 mod 2, 3 mod 3 = 0^2 mod 3, terminates at 3 mod 5 (nonsquare).
a(3) = 4: |{0, 1, 4}| = 3.
a(4) = 184: |{0, 1, 4, 2}| = 4 (2 = 3^2 mod 7).
a(5) = 9: |{1, 0, 4, 2, 9}| = 5.
a(6) = 1479: |{1, 0, 4, 2, 5, 10}| = 6.

Prog

(PARI) a(n)={my(v=List); for(k=1, oo, my(m=Map); for(i=1, oo, my(p=prime(i), kp=k%p); if(i>#v, listput(v, Map); for(j=0, (p-p%2)/2, mapput(v[i], j^2%p, 1))); if(mapisdefined(v[i], kp) && !mapisdefined(m, kp), mapput(m, kp, 1); next); if(i-1==n, return(k)); break))}

Crossrefs

Cf. A377212 (nondistinct squares), A385051 (distinct nonsquares), A279074 (distinct moduli).

Sequence in context: A041903 A156513 A082213 * A097172 A042081 A245456

Adjacent sequences: A385047 A385048 A385049 * A385051 A385052 A385053

Keyword

nonn

Author

Charles L. Hohn, Jun 16 2025

Status

approved