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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 2 19:34 EST 2023. Contains 360024 sequences. (Running on oeis4.)