A055260 - OEIS

%I #17 Feb 11 2021 04:59:33

%S 2,10,18,82,90,162,730,738,810,1458,6562,6570,6642,7290,13122,59050,

%T 59058,59130,59778,65610,118098,531442,531450,531522,532170,538002,

%U 590490,1062882,4782970,4782978,4783050,4783698,4789530,4842018,5314410,9565938,43046722

%N Sums of two powers of 9.

%H T. D. Noe, <a href="/A055260/b055260.txt">Rows n = 0..100 of triangle, flattened</a>

%F 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)

%F Regarded as a triangle T(n, k) = 9^n + 9^k, so as a sequence a(n) = 9^A002262(n) + 9^A003056(n).

%t t = 9^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* _T. D. Noe_, Oct 09 2011 *)

%t Total/@Tuples[9^Range[0,10],2]//Union (* _Harvey P. Dale_, Jul 03 2019 *)

%o (Python)

%o def valuation(n, b):

%o   v = 0

%o   while n > 1: n //= b; v += 1

%o   return v

%o def aupto(lim):

%o   pows = [9**i for i in range(valuation(lim-1, 9) + 1)]

%o   sum_pows = sorted([a+b for i, a in enumerate(pows) for b in pows[i:]])

%o   return [s for s in sum_pows if s <= lim]

%o print(aupto(43046722)) # _Michael S. Branicky_, Feb 10 2021

%Y Cf. A001019, A052216.

%K easy,nonn,tabl

%O 0,1

%A _Henry Bottomley_, Jun 22 2000