A145049 Primes p of the form 4k+1 for which s=17 is the least positive integer such that sp-(floor(sqrt(sp)))^2 is a square.

3037, 3169, 3257, 3769, 4013, 4421, 4793, 4957, 5237, 5297, 5701, 5821, 5881, 6373, 6689, 6761, 6949, 7013, 7213, 7417, 7481, 7549, 7621, 7757, 8389, 8461, 8537, 8681, 8753, 9049, 9133, 9277, 9349, 9733, 10133, 10529, 10601, 11093, 11177, 11257, 11677, 11701

Offset: 1

Author

Vladimir Shevelev, Sep 30 2008

Keywords

• nonn

Examples

			a(1)=3037 since p=3037 is the least prime of the form 4k+1 for which sp-(floor(sqrt(sp)))^2 is not a square for s=1..16, but 17p-(floor(sqrt(17p)))^2 is a square (for p=3037 it is 100).
		

Links

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

Crossrefs

Cf. A145016, A145022, A145023, A145047, A145048.

Programs

Maple

filter:= proc(p) local s;
  if not isprime(p) then return false fi;
  for s from 1 to 17 do
    if issqr(s*p - floor(sqrt(s*p))^2) then return evalb(s=17) fi
  od;
  false
end proc:
select(filter, [seq(i,i=1..10000,4)]); # Robert Israel, Jan 22 2024