cp's OEIS Frontend

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

%I A249875 #20 Dec 27 2023 15:48:17
%S A249875 3,6,34,136,498,2082,8146,32946,131058,524232,2096928,8387712,
%T A249875 33550848,134226562,536859906,2147439624,8589943858,34359775432,
%U A249875 137439101728,549756406912,2199022661826,8796090647304,35184374452498,140737497809992,562949943786834,2251799775147336
%N A249875 Numbers that are exactly halfway between the nearest square and the nearest power of 2.
%C A249875 Numbers that are the arithmetic mean of the nearest square and the nearest power of 2 (other than that nearest square).
%H A249875 Chai Wah Wu, <a href="/A249875/b249875.txt">Table of n, a(n) for n = 1..501</a>
%e A249875 3 is a term because 2<3<4; 6 is a term because 4<6<8.
%o A249875 (Python)
%o A249875 def isqrt(a):
%o A249875     sr = 1 << (a.bit_length() >> 1)
%o A249875     while a < sr * sr:
%o A249875         sr >>= 1
%o A249875     b = sr >> 1
%o A249875     while b:
%o A249875         s = sr + b
%o A249875         if a >= s * s:
%o A249875             sr = s
%o A249875         b >>= 1
%o A249875     return sr
%o A249875 for j in range(99):
%o A249875     i = 2**j
%o A249875     r = isqrt(i)
%o A249875     if r * r == i:
%o A249875         continue
%o A249875     if r & 1:
%o A249875         a = ((r + 1) * (r + 1) + i) // 2
%o A249875     else:
%o A249875         a = (i + r * r) // 2
%o A249875     print(a, end=', ')
%o A249875 (Python)
%o A249875 from gmpy2 import isqrt
%o A249875 A249875_list, x = [], 1
%o A249875 for _ in range(10**3):
%o A249875     A249875_list.append(2*sum(divmod(isqrt(2*x),2))**2+x)
%o A249875     x *= 4 # _Chai Wah Wu_, Dec 16 2014
%Y A249875 Cf. A000290, A000079, A233074, A233075.
%K A249875 nonn
%O A249875 1,1
%A A249875 _Alex Ratushnyak_, Nov 07 2014