A375202 -id:A375202 - cp's OEIS frontend

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

Robert Israel, Oct 15 2024

nonn

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

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

Chai Wah Wu, Table of n, a(n) for n = 1..52
Mathematics StackExchange, Large smallest square in a sum of three squares?

Cf. A375202, A375204.

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;

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

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

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

A375204 Record values in A375202.

Original entry on oeis.org

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

Robert Israel, Oct 15 2024

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

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

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

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

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;

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

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

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

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

cp's OEIS Frontend

A375203 Positions of records in A375202.

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