A145049 - OEIS

%I #11 Jan 23 2024 09:20:50

%S 3037,3169,3257,3769,4013,4421,4793,4957,5237,5297,5701,5821,5881,

%T 6373,6689,6761,6949,7013,7213,7417,7481,7549,7621,7757,8389,8461,

%U 8537,8681,8753,9049,9133,9277,9349,9733,10133,10529,10601,11093,11177,11257,11677,11701

%N 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.

%H Robert Israel, <a href="/A145049/b145049.txt">Table of n, a(n) for n = 1..10000</a>

%e 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).

%p filter:= proc(p) local s;

%p   if not isprime(p) then return false fi;

%p   for s from 1 to 17 do

%p     if issqr(s*p - floor(sqrt(s*p))^2) then return evalb(s=17) fi

%p   od;

%p   false

%p end proc:

%p select(filter, [seq(i,i=1..10000,4)]); # _Robert Israel_, Jan 22 2024

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

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Sep 30 2008