A055261 Sums of two powers of 16.

2, 17, 32, 257, 272, 512, 4097, 4112, 4352, 8192, 65537, 65552, 65792, 69632, 131072, 1048577, 1048592, 1048832, 1052672, 1114112, 2097152, 16777217, 16777232, 16777472, 16781312, 16842752, 17825792, 33554432, 268435457

Offset: 1

Author

Henry Bottomley, Jun 22 2000

Keywords

• base
• easy
• nonn
• tabl

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052216.

Programs

Maple

A055261:= proc(n)
     local p1, p2;
     p1:= floor((sqrt(8*n-7)-1)/2);
     p2:= n - 1 - p1*(p1+1)/2;
     16^p1 + 16^p2
end proc; # Robert Israel, Apr 07 2014

Python

from math import isqrt
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

Formula

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).

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