A385051 a(n) is the least positive number k such that n is the greatest m such that k is a quadratic nonresidue mod prime(i+1) for i=1..m and {k mod prime(i+1): i=1..m} are all distinct.

1, 2, 8, 68, 173, 593, 1748, 908, 40178, 74093, 91538, 93308, 441803, 10712063, 7898483, 35865968, 133019963, 206951093, 1314259253, 2453647853, 6701493818, 54776939873, 7717930358, 250589717363, 255937042268, 3665861003153, 957987212453, 9953155219223

Offset

0,2

Comments

Only relevant for odd primes, as every positive integer is a square mod 2.

For n >= 3, {a(n) mod 105} = {68, 83}.

Links

Table of n, a(n) for n=0..27.

Example

a(0) = 1: |{}| = 0: terminates at 1 mod 3 (square: = 1^2 mod 3).
a(1) = 2: |{2}| = 1: 2 mod 3 = 2 (nonsquare), terminates at 2 mod 5 (not distinct: repeats 2 mod 3).
a(2) = 8: |{2, 3}| = 2: 8 mod 3 = 2 (nonsquare), 8 mod 5 = 3 (nonsquare), terminates at 8 mod 7 (square: = 1^2 mod 7).
a(3) = 68: |{2, 3, 5}| = 3.

Prog

(PARI) a(n)={my(v=List); for(k=1, oo, my(m=Map); for(i=1, oo, my(p=prime(i+1), 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. A376999 (nondistinct nonsquares), A385050 (distinct squares), A279074 (distinct moduli).

Sequence in context: A202553 A023164 A053922 * A030445 A093990 A393837

Adjacent sequences: A385048 A385049 A385050 * A385052 A385053 A385054

Keyword

nonn

Author

Charles L. Hohn, Jun 16 2025

Status

approved