A376999 a(n) is the least number k that is a quadratic residue modulo prime(n) but is a quadratic nonresidue modulo all previous odd primes.

0, 5, 2, 38, 17, 83, 362, 167, 227, 2273, 398, 5297, 64382, 69467, 116387, 238262, 214037, 430022, 5472953, 9481097, 8062073, 41941577, 86374763, 312521282

Offset

2,2

Links

Table of n, a(n) for n=2..25.

Example

a(5) = 38 because 38 is a quadratic residue modulo prime(5) = 11 but is not a quadratic residue modulo the previous odd primes 3, 5 and 7, and no number smaller than 38 works.

Maple

f:= proc(n) local k, p;
  p:= 2;
  for k from 2 do
      p:= nextprime(p);
      if numtheory:-quadres(n, p) = 1 then return k fi
  od
end proc:
V:= Array(2..25): count:= 0:
for k from 2 while count < 24 do
  v:= f(k);
if v > 0 and v <= 25 and V[v] = 0 then
  V[v]:= k; count:= count+1;
fi;
od:
V[2]:= 0:
convert(V, list);

Crossrefs

Cf. A377212.

Sequence in context: A095998 A328555 A208927 * A099612 A233044 A142599

Adjacent sequences: A376996 A376997 A376998 * A377000 A377001 A377002

Keyword

nonn

Author

Robert Israel, Oct 20 2024

Status

approved