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A249875
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Numbers that are exactly halfway between the nearest square and the nearest power of 2.
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1
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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
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internal format)
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OFFSET
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1,1
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COMMENTS
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Numbers that are the arithmetic mean of the nearest square and the nearest power of 2 (other than that nearest square).
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LINKS
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EXAMPLE
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3 is a term because 2<3<4; 6 is a term because 4<6<8.
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PROG
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(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
for _ in range(10**3):
A249875_list.append(2*sum(divmod(isqrt(2*x), 2))**2+x)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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