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

Author

Alex Ratushnyak, Nov 07 2014

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000290, A000079, A233074, A233075.

Programs

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