A377380 a(n) is the first positive number k such that k is alternately a quadratic residue and nonresidue modulo the first n primes, but not the n+1'th.

1, 2, 11, 41, 26, 5, 671, 89, 59, 1181, 1991, 3755, 21521, 34145, 25994, 137885, 61106, 1503029, 2617439, 1008551, 2897081, 22363295, 33603926, 36518450, 79865294, 185914490, 593068985, 2211452939, 2120224529, 1673286179, 2644173521, 1976870465

Offset

1,2

Comments

a(n) == 2 (mod 3) for n >= 2.

Links

Table of n, a(n) for n=1..32.

Example

a(3) = 11 because 11 is a quadratic residue mod 2, a nonresidue mod 3, a residue mod 5, but a residue mod 7, and no smaller number works.

Maple

with(numtheory):
N:= 20:
V:= Vector(N): V[1]:= 1: count:= 1:
for x from 2 by 3 while count < N do
  p:= 1:
  for m from 0 do
    p:= nextprime(p);
    if numtheory:-quadres(x, p) <> (-1)^m then break fi;
  od;
  if V[m] = 0 then
    V[m]:= x; count:= count+1;
  fi
od:
convert(V, list);

Crossrefs

Cf. A096636, A377212.

Sequence in context: A335629 A000822 A290175 * A154813 A168367 A247101

Adjacent sequences: A377377 A377378 A377379 * A377381 A377382 A377383

Keyword

nonn

Author

Robert Israel, Oct 27 2024

Status

approved