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

Author

Charles L. Hohn, Jun 16 2025

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Crossrefs

Cf. A376999 (nondistinct nonsquares), A385050 (distinct squares), A279074 (distinct moduli).

Programs

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))}