A249875 Numbers that are exactly halfway between the nearest square and the nearest power of 2.

3, 6, 34, 136, 498, 2082, 8146, 32946, 131058, 524232, 2096928, 8387712, 33550848, 134226562, 536859906, 2147439624, 8589943858, 34359775432, 137439101728, 549756406912, 2199022661826, 8796090647304, 35184374452498, 140737497809992, 562949943786834, 2251799775147336

Offset

1,1

Comments

Numbers that are the arithmetic mean of the nearest square and the nearest power of 2 (other than that nearest square).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..501

Example

3 is a term because 2<3<4; 6 is a term because 4<6<8.

Prog

(Python)
def isqrt(a):
    sr = 1 << (a.bit_length() >> 1)
    while a < sr * sr:
        sr >>= 1
    b = sr >> 1
    while b:
        s = sr + b
        if a >= s * s:
            sr = s
        b >>= 1
    return sr
for j in range(99):
    i = 2**j
    r = isqrt(i)
    if r * r == i:
        continue
    if r & 1:
        a = ((r + 1) * (r + 1) + i) // 2
    else:
        a = (i + r * r) // 2
    print(a, end=', ')
(Python)
from gmpy2 import isqrt
A249875_list, x = [], 1
for _ in range(10**3):
    A249875_list.append(2*sum(divmod(isqrt(2*x), 2))**2+x)
    x *= 4 # Chai Wah Wu, Dec 16 2014

Crossrefs

Cf. A000290, A000079, A233074, A233075.

Sequence in context: A375448 A186750 A203715 * A308557 A134748 A068904

Adjacent sequences: A249872 A249873 A249874 * A249876 A249877 A249878

Keyword

nonn

Author

Alex Ratushnyak, Nov 07 2014

Status

approved