A375204 Record values in A375202.

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 32, 36, 40, 48, 64, 72, 80, 96, 128, 144, 160, 192, 256, 288, 320, 384, 512, 576, 640, 768, 1024, 1152, 1280, 1536, 2048, 2304, 2560, 3072, 4096, 4608, 5120, 6144, 8192, 9216, 10240, 12288, 16384

Offset: 1

Author

Robert Israel, Oct 15 2024

Keywords

• nonn
• more

Comments

Numbers k such that k = A375202(m) for some m such that A375202(j) < k for all j < m.

Conjectures: All powers of 2 (A000079), 3*(powers of 2) (A007283) and 5*(powers of 2) (A020714) are terms. All terms are 5-smooth (A051037). - Chai Wah Wu, Oct 16 2024

Examples

			a(3) = 2 because A375202(12) = 2 and A375202(j) <= 1 for j < 12.
		

Links

• Mathematics StackExchange, Large smallest square in a sum of three squares?

Crossrefs

Cf. A000079, A007283, A020714, A051037, A375202, A375203.

Programs

Maple

f:= proc(n) local q, x, y, z;
  if n/4^padic:-ordp(n, 4) mod 8 = 7 then return -1 fi;
  for x from 0 while 3*x^2 <= n do
    if [isolve(y^2 + z^2 = n - x^2)] <> [] then return x fi
  od;
end proc:
V:= NULL:count:= 0: m:= -1;
for i from 0 while count < 39 do
  v:= f(i);
  if v > m then
    V:= V, v; m:= v; count:=count+1
  fi
od:
V;

Python

from itertools import count, islice
from math import isqrt
from sympy import factorint
def A375204_gen(): # generator of terms
    c = -1
    for n in count(0):
        v = (~n & n-1).bit_length()
        if v&1 or n>>v&7!=7:
            a = next(x for x in range(isqrt(n//3)+1) if not any(e&1 and p&3==3 for p, e in factorint(n-x**2).items()))
            if a>c:
                yield a
                c = a
A375204_list = list(islice(A375204_gen(),20)) # Chai Wah Wu, Oct 16 2024

Formula

a(n) = A375292(A375203(n)).

Extensions

a(35)-a(48) from Chai Wah Wu, Oct 16 2024

a(49)-a(52) from Chai Wah Wu, Oct 17 2024