A233444 Primes that are exactly halfway between the nearest square and the nearest cube.

2203, 90863, 185477, 388573, 613607, 912349, 1293899, 1600919, 2146457, 30661333, 35608189, 81190429, 105823093, 122753857, 204341747, 338602837, 368601707, 374788121, 426958673, 498675409, 586371239, 656232799, 665360321, 674509487, 693132527, 1102304669, 1180942709

Offset: 1

Author

Alex Ratushnyak, Dec 09 2013

Keywords

• nonn

Comments

A subsequence of A233075.

Links

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

Crossrefs

Cf. A000040, A000290, A000578, A233075.

Cf. A002760 (Squares and cubes).

Programs

Maple

Res:= NULL:
for x from 3 to 2000 do
  x3:= x^3;
  y:= floor(sqrt(x3));
  p:= (x3+y^2)/2;
  if p::integer and x3-p <= p - (x-1)^3 and p - y^2 <= (y+1)^2-p and isprime(p) then
    Res:= Res, p;
  fi;
  p:= (x3+(y+1)^2)/2;
  if p::integer and p-x3 <= (x+1)^3-p and (y+1)^2-p <= p - y^2 and isprime(p) then
      Res:= Res, p;
  fi
od:
Res; # Robert Israel, May 01 2018