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A145022 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. 14
41, 61, 89, 113, 149, 157, 181, 193, 233, 269, 277, 313, 317, 337, 389, 421, 433, 557, 569, 613, 617, 709, 761, 773, 853, 881, 929, 937, 1013, 1109, 1117, 1129, 1201, 1213, 1301, 1409, 1429, 1553, 1637, 1741, 1753, 1861, 1873, 1901, 1997, 2113, 2137, 2153 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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).

MAPLE

filter:= proc(p)

  if not isprime(p) then return false fi;

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

  issqr(2*p-floor(sqrt(2*p))^2)

end proc:

select(filter, [seq(p, p=1..10000, 4)]); # Robert Israel, Dec 04 2018

MATHEMATICA

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 *)

CROSSREFS

Cf. A145016.

Sequence in context: A178057 A169798 A110411 * A154763 A141881 A139952

Adjacent sequences:  A145019 A145020 A145021 * A145023 A145024 A145025

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Sep 29 2008

STATUS

approved

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Last modified May 7 00:22 EDT 2021. Contains 343609 sequences. (Running on oeis4.)