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

1,3

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

Links

Table of n, a(n) for n=1..52.

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

Formula

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

Example

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

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;

Prog

(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

Crossrefs

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

Sequence in context: A367501 A367463 A052347 * A193299 A022773 A049997

Adjacent sequences: A375201 A375202 A375203 * A375205 A375206 A375207

Keyword

nonn,more

Author

Robert Israel, Oct 15 2024

Extensions

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

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

Status

approved