A328803 The minimum value of j + k where j and k are positive integers with j^2 + k^2 = A001481(n).

0, 1, 2, 2, 3, 4, 3, 4, 5, 4, 5, 6, 6, 5, 6, 7, 8, 8, 6, 7, 8, 9, 9, 7, 8, 10, 9, 10, 11, 8, 9, 10, 12, 11, 12, 12, 9, 10, 11, 13, 12, 13, 14, 10, 11, 12, 14, 13, 15, 14, 15, 11, 12, 13, 16, 14, 16, 15, 12, 13, 16, 14, 17, 15, 17, 16, 18, 18, 13, 14, 15, 16

Offset: 1

Author

Peter Kagey, Oct 27 2019

Keywords

• nonn
• look

Examples

			For n = 14, A001481(14) = 25 = 0^2 + 5^2 = 3^2 + 4^2, so a(14) = min{0+5, 3+4} = 5.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000161, A001481.

Programs

Maple

N:= 1000: # for terms where A001481(n)<=N
for s from 0 to isqrt(N) do
   for i from 0 to s/2 do
      t:= i^2 + (s-i)^2;
      if t > N then break fi;
      if not assigned(R[t]) then R[t]:= s fi;
od od:
A1481:= sort(map(op, [indices(R)])):
seq(R[i],i=A1481); # Robert Israel, Oct 28 2019

Python

from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
from sympy import factorint
def A328803_gen(): # generator of terms
    return map(lambda n: min((a+b for a, b in diop_DN(-1,n))), filter(lambda n:(lambda m:all(d&3!=3 or m[d]&1==0 for d in m))(factorint(n)), count(0)))
A328803_list = list(islice(A328803_gen(),30)) # Chai Wah Wu, Sep 09 2022