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 A029955 Palindromic in base 9. 32
 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 82, 91, 100, 109, 118, 127, 136, 145, 154, 164, 173, 182, 191, 200, 209, 218, 227, 236, 246, 255, 264, 273, 282, 291, 300, 309, 318, 328, 337, 346, 355, 364, 373, 382, 391, 400, 410, 419, 428, 437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 03 2020 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Javier Cilleruelo, Florian Luca and Lewis Baxter, Every positive integer is a sum of three palindromes, Mathematics of Computation, Vol. 87, No. 314 (2018), pp. 3023-3055, arXiv preprint, arXiv:1602.06208 [math.NT], 2017. Patrick De Geest, Palindromic numbers beyond base 10. Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019. Index entries for sequences that are an additive basis, order 3. FORMULA Sum_{n>=2} 1/a(n) = 3.29797695... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020 MATHEMATICA f[n_, b_] := Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 9], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *) PROG (Python) from gmpy2 import digits def palQgen(l, b): # generator of palindromes in base b of length <= 2*l if l > 0: yield 0 for x in range(1, l+1): for y in range(b**(x-1), b**x): s = digits(y, b) yield int(s+s[-2::-1], b) for y in range(b**(x-1), b**x): s = digits(y, b) yield int(s+s[::-1], b) A029955_list = list(palQgen(4, 9)) # Chai Wah Wu, Dec 01 2014 (Python) from gmpy2 import digits def A029955(n): if n == 1: return 0 y = 9*(x:=9**(len(digits(n>>1, 9))-1)) return int((c:=n-x)*x+int(digits(c, 9)[-2::-1]or'0', 9) if n

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