A145022 - OEIS

%I #14 Jan 12 2020 23:45:43

%S 41,61,89,113,149,157,181,193,233,269,277,313,317,337,389,421,433,557,

%T 569,613,617,709,761,773,853,881,929,937,1013,1109,1117,1129,1201,

%U 1213,1301,1409,1429,1553,1637,1741,1753,1861,1873,1901,1997,2113,2137,2153

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

%H Robert Israel, <a href="/A145022/b145022.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1)=41 since p=41 is the least prime of the form 4k+1 for which p-(floor(sqrt(p)))^2 is not a square, but 2p-(floor(sqrt(2p)))^2 is a square (for p=41 it is 1).

%p filter:= proc(p)

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

%p   if issqr(p-floor(sqrt(p))^2) then return false fi;

%p   issqr(2*p-floor(sqrt(2*p))^2)

%p end proc:

%p select(filter, [seq(p,p=1..10000,4)]); # _Robert Israel_, Dec 04 2018

%t sQ[n_] := IntegerQ[Sqrt[n - (Floor[Sqrt[n]])^2]]; aQ[n_] := Mod[n, 4] == 1 && PrimeQ[n] && !sQ[n] && sQ[2n]; Select[Range[2200], aQ] (* _Amiram Eldar_, Dec 04 2018 *)

%Y Cf. A145016.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Sep 29 2008