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Sums of two powers of 16.
5

%I #11 Apr 07 2014 03:11:48

%S 2,17,32,257,272,512,4097,4112,4352,8192,65537,65552,65792,69632,

%T 131072,1048577,1048592,1048832,1052672,1114112,2097152,16777217,

%U 16777232,16777472,16781312,16842752,17825792,33554432,268435457

%N Sums of two powers of 16.

%H Robert Israel, <a href="/A055261/b055261.txt">Table of n, a(n) for n = 1..10000</a>

%F 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 Regarded as a triangle T(n, k)=16^n+16^k, so as a sequence a(n) =16^A002262(n)+16^A003056(n).

%e a(4) = 272 = 16^2+16^1.

%p A055261:= proc(n)

%p local p1, p2;

%p p1:= floor((sqrt(8*n-7)-1)/2);

%p p2:= n - 1 - p1*(p1+1)/2;

%p 16^p1 + 16^p2

%p end proc; # _Robert Israel_, Apr 07 2014

%Y Cf. A052216.

%K base,easy,nonn,tabl

%O 1,1

%A _Henry Bottomley_, Jun 22 2000