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

1,1

Links

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

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).

Example

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

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

Prog

(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

Crossrefs

Cf. A052216.

Sequence in context: A212740 A212742 A178145 * A307690 A100294 A192453

Adjacent sequences: A055258 A055259 A055260 * A055262 A055263 A055264

Keyword

base,easy,nonn,tabl

Author

Henry Bottomley, Jun 22 2000

Status

approved