login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
7
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
1,1
LINKS
EXAMPLE
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).
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 30 2008
STATUS
approved