cp's OEIS Frontend

A055261 Sums of two powers of 16.

%I A055261 #14 Apr 08 2025 17:15:19
%S A055261 2,17,32,257,272,512,4097,4112,4352,8192,65537,65552,65792,69632,
%T A055261 131072,1048577,1048592,1048832,1052672,1114112,2097152,16777217,
%U A055261 16777232,16777472,16781312,16842752,17825792,33554432,268435457
%N A055261 Sums of two powers of 16.
%H A055261 Robert Israel, <a href="/A055261/b055261.txt">Table of n, a(n) for n = 1..10000</a>
%F A055261 a(n) = 16^(n-trinv(n))+16^trinv(n), where trinv(n) = floor((1+sqrt(1+8*n))/2) = A002262(n) and n-trinv(n) = A003056(n).
%F A055261 Regarded as a triangle T(n, k)=16^n+16^k, so as a sequence a(n) =16^A002262(n)+16^A003056(n).
%e A055261 a(4) = 272 = 16^2+16^1.
%p A055261 A055261:= proc(n)
%p A055261      local p1, p2;
%p A055261      p1:= floor((sqrt(8*n-7)-1)/2);
%p A055261      p2:= n - 1 - p1*(p1+1)/2;
%p A055261      16^p1 + 16^p2
%p A055261 end proc; # _Robert Israel_, Apr 07 2014
%o A055261 (Python)
%o A055261 from math import isqrt
%o A055261 def A055261(n): return (1<<((a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)<<2))+(1<<(n-1-(a*(a+1)>>1)<<2)) # _Chai Wah Wu_, Apr 08 2025
%Y A055261 Cf. A052216.
%K A055261 base,easy,nonn,tabl
%O A055261 1,1
%A A055261 _Henry Bottomley_, Jun 22 2000