A377380 - OEIS

%I #11 Oct 27 2024 10:46:30

%S 1,2,11,41,26,5,671,89,59,1181,1991,3755,21521,34145,25994,137885,

%T 61106,1503029,2617439,1008551,2897081,22363295,33603926,36518450,

%U 79865294,185914490,593068985,2211452939,2120224529,1673286179,2644173521,1976870465

%N 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.

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

%e 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.

%p with(numtheory):

%p N:= 20:

%p V:= Vector(N): V[1]:= 1: count:= 1:

%p for x from 2 by 3 while count < N do

%p   p:= 1:

%p   for m from 0 do

%p     p:= nextprime(p);

%p     if numtheory:-quadres(x,p) <> (-1)^m then break fi;

%p   od;

%p   if V[m] = 0 then

%p     V[m]:= x; count:= count+1;

%p   fi

%p od:

%p convert(V,list);

%Y Cf. A096636, A377212.

%K nonn

%O 1,2

%A _Robert Israel_, Oct 27 2024