A363761 a(n) is the least k < 3*n such that there are exactly n distinct numbers j that can be expressed as sum of two squares with k^2 < j < (k+1)^2, or -1 if such a k does not exist.

0, 1, 2, 4, 5, 7, 8, 10, 13, 12, 15, 17, 19, 23, 21, 24, 25, 28, 32, 31, 34, 37, 39, 44, 41, 43, 45, 50, 51, 48, 57, 55, 56, 59, 64, 63, 68, 69, 74, 77, 78, 75, 72, 80, 88, 84, -1, 94, 89, 96, 93, 99, 97, 102, 108, -1, 106, 111, 110, 113, 117, 120, -1, 123, 133, 127, 130, 137, 142, 138, 139, -1, 135

Offset

0,3

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..3000

Formula

If a(n) != -1, then a(n) >= n/2. - Chai Wah Wu, Jun 22 2023

a(n) = A363763(n) for n <= 11459.

a(n) = -1 for n > 15898.

Prog

(PARI) a363761(upto) = {for (n=0, upto, my(kfound=-1);
for (k=0, 3*n, my(k1=k^2+1, k2=k*(k+2), m=0);
for (j=k1, k2, m+= (sumdiv(j, d, (d%4==1)-(d%4==3))>0); if (m>n, break));
if (m==n, kfound=k; break); if (m==n, kfound=k; break)); print1(kfound, ", "))};
a363761(75)
(Python)
from sympy import factorint
def A363761(n):
    for k in range(n>>1, 3*n):
        c = 0
        for m in range(k**2+1, (k+1)**2):
            if all(p==2 or p&3==1 or e&1^1 for p, e in factorint(m).items()):
                c += 1
                if c>n:
                    break
        if c==n:
            return k
    return -1 # Chai Wah Wu, Jun 22 2023

Crossrefs

Cf. A001481, A004018, A077773, A363762.

Identical with A363763 for n <= 11459, but increasingly different afterwards, i.e., a(11460) = -1, whereas A363763(11460) = 34451.

Sequence in context: A248566 A091627 A160830 * A363763 A189303 A192817

Adjacent sequences: A363758 A363759 A363760 * A363762 A363763 A363764

Keyword

sign

Author

Hugo Pfoertner, Jun 22 2023

Status

approved