A055260 Sums of two powers of 9.

2, 10, 18, 82, 90, 162, 730, 738, 810, 1458, 6562, 6570, 6642, 7290, 13122, 59050, 59058, 59130, 59778, 65610, 118098, 531442, 531450, 531522, 532170, 538002, 590490, 1062882, 4782970, 4782978, 4783050, 4783698, 4789530, 4842018, 5314410, 9565938, 43046722

Offset

0,1

Links

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

Formula

a(n) = 9^(n-trinv(n))+9^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) = 9^n + 9^k, so as a sequence a(n) = 9^A002262(n) + 9^A003056(n).

Mathematica

t = 9^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* T. D. Noe, Oct 09 2011 *)
Total/@Tuples[9^Range[0, 10], 2]//Union (* Harvey P. Dale, Jul 03 2019 *)

Prog

(Python)
def valuation(n, b):
  v = 0
  while n > 1: n //= b; v += 1
  return v
def aupto(lim):
  pows = [9**i for i in range(valuation(lim-1, 9) + 1)]
  sum_pows = sorted([a+b for i, a in enumerate(pows) for b in pows[i:]])
  return [s for s in sum_pows if s <= lim]
print(aupto(43046722)) # Michael S. Branicky, Feb 10 2021

Crossrefs

Cf. A001019, A052216.

Sequence in context: A271786 A134251 A317714 * A254059 A346551 A180591

Adjacent sequences: A055257 A055258 A055259 * A055261 A055262 A055263

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Jun 22 2000

Status

approved