A375203 Positions of records in A375202.

0, 3, 12, 43, 48, 142, 172, 192, 427, 568, 688, 768, 1708, 2272, 2752, 3072, 6832, 9088, 11008, 12288, 27328, 36352, 44032, 49152, 109312, 145408, 176128, 196608, 437248, 581632, 704512, 786432, 1748992, 2326528, 2818048, 3145728, 6995968, 9306112, 11272192

Offset

1,2

Comments

Numbers k such that the A375202(k) > A375202(j) for all j < k.

Links

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

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

Formula

A375202(a(n)) = A375204(n).

Example

a(3) = 12 is a term 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:
R:= NULL:count:= 0: m:= -1;
for i from 0 while count < 39 do
  v:= f(i);
  if v > m then
    R:= R, i; m:= v; count:=count+1
  fi
od:
R;

Prog

(Python)
from itertools import count, islice
from math import isqrt
from sympy import factorint
def A375203_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 n
                c = a
A375203_list = list(islice(A375203_gen(), 20)) # Chai Wah Wu, Oct 16 2024

Crossrefs

Cf. A375202, A375204.

Sequence in context: A191112 A066987 A366617 * A290918 A012873 A282082

Adjacent sequences: A375200 A375201 A375202 * A375204 A375205 A375206

Keyword

nonn

Author

Robert Israel, Oct 15 2024

Extensions

a(35)-a(39) from Chai Wah Wu, Oct 16 2024

Status

approved