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A309759 Numbers that are sums of consecutive powers of 4.

%I A309759 #15 Apr 04 2025 14:36:55
%S A309759 1,4,5,16,20,21,64,80,84,85,256,320,336,340,341,1024,1280,1344,1360,
%T A309759 1364,1365,4096,5120,5376,5440,5456,5460,5461,16384,20480,21504,21760,
%U A309759 21824,21840,21844,21845,65536,81920,86016,87040,87296,87360,87376,87380
%N A309759 Numbers that are sums of consecutive powers of 4.
%C A309759 Numbers of the form (4^i - 4^j)/3 with i > j.
%H A309759 Harvey P. Dale, <a href="/A309759/b309759.txt">Table of n, a(n) for n = 1..1000</a>
%e A309759 336 = 4^2 + 4^3 + 4^4, so 336 is in the sequence.
%e A309759 +------+--------+
%e A309759 | a(n) | base 4*|
%e A309759 +------+--------+
%e A309759 |   1  |     1  |
%e A309759 |   4  |    10  |
%e A309759 |   5  |    11  |
%e A309759 |  16  |   100  |
%e A309759 |  20  |   110  |
%e A309759 |  21  |   111  |
%e A309759 |  64  |  1000  |
%e A309759 |  80  |  1100  |
%e A309759 |  84  |  1110  |
%e A309759 |  85  |  1111  |
%e A309759 +------+--------+
%e A309759 * - a(n) written in base 4.
%t A309759 Module[{nn=10,k},k=4^Range[0,nn];Table[Accumulate[Reverse[Take[k,n]]],{n,nn}]]//Flatten (* _Harvey P. Dale_, May 29 2021 *)
%o A309759 (Python)
%o A309759 from math import isqrt
%o A309759 def A309759(n): return ((1<<((m:=isqrt(n<<3)+1>>1)<<1))-(1<<m*(m+1)-(n<<1)&-2))//3 # _Chai Wah Wu_, Apr 04 2025
%Y A309759 Cf. A000302, A000695, A023758, A038470, A309758, A309761.
%K A309759 nonn
%O A309759 1,2
%A A309759 _Ilya Gutkovskiy_, Aug 15 2019