A055259 Sums of two powers of 8.

2, 9, 16, 65, 72, 128, 513, 520, 576, 1024, 4097, 4104, 4160, 4608, 8192, 32769, 32776, 32832, 33280, 36864, 65536, 262145, 262152, 262208, 262656, 266240, 294912, 524288, 2097153, 2097160, 2097216, 2097664, 2101248, 2129920, 2359296, 4194304, 16777217

Offset

0,1

Links

T. D. Noe, Rows n = 0..100 of triangle, flattened

Formula

a(n) = 8^(n-trinv(n))+8^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) = 8^n + 8^k, so as a sequence a(n) = 8^A002262(n) + 8^A003056(n).

Mathematica

Union[Total/@Tuples[8^Range[0, 10], {2}]]  (* Harvey P. Dale, Mar 13 2011 *)

Prog

(Python)
def valuation(n, b):
  v = 0
  while n > 1: n //= b; v += 1
  return v
def aupto(lim):
  pows8 = [8**i for i in range(valuation(lim-1, 8) + 1)]
  sum_pows8 = sorted([a+b for i, a in enumerate(pows8) for b in pows8[i:]])
  return [s for s in sum_pows8 if s <= lim]
print(aupto(16777217)) # Michael S. Branicky, Feb 09 2021

Crossrefs

Cf. A052216.

Sequence in context: A304974 A075645 A185252 * A032299 A032211 A032136

Adjacent sequences: A055256 A055257 A055258 * A055260 A055261 A055262

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Jun 22 2000

Status

approved