A204919 a(n) = q^2 where q is the least prime such that n divides A204916(n)^2 - q^2.

4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 49, 4, 9, 4, 25, 289, 25, 4, 49, 4, 9, 4, 49, 4, 25, 4, 121, 9, 49, 961, 49, 4, 9, 4, 121, 4, 25, 4, 289, 1681, 25, 4, 361, 4, 49, 2209, 529, 4, 9, 4, 289, 4, 49

Offset: 1

Author

Clark Kimberling, Jan 20 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A204892.

Original name was "Least prime q^2 such that n divides p^2-q^2 for some prime p>q", which would be A089090. - Robert Israel, May 04 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A089090, A204916, A204908, A204900, A204892.

Programs

Maple

N:= 100: # to get a(1)..a(N)
A:= Vector(N): count:= 0:
p:= 2: P:= 2:
for i from 1 while count < N do
  p:= nextprime(p);
  ps:= p^2;
  P:= P, p;
  for j from 1 to i while count < N do
   qs:= P[j]^2;
   S:= convert(select(t -> t <= N and A[t]=0, numtheory:-divisors(ps-qs)),list);
   A[S]:= qs;
   count:= count + nops(S);
od od:
convert(A,list); # Robert Israel, May 04 2019

Mathematica

(See the program at A204916.)

Extensions

Name corrected by Robert Israel, May 04 2019