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A055260
Sums of two powers of 9.
5
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
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
Sequence in context: A271786 A134251 A317714 * A254059 A346551 A180591
KEYWORD
easy,nonn,tabl
AUTHOR
Henry Bottomley, Jun 22 2000
STATUS
approved