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A029953
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Palindromic in base 6.
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28
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0, 1, 2, 3, 4, 5, 7, 14, 21, 28, 35, 37, 43, 49, 55, 61, 67, 74, 80, 86, 92, 98, 104, 111, 117, 123, 129, 135, 141, 148, 154, 160, 166, 172, 178, 185, 191, 197, 203, 209, 215, 217, 259, 301, 343, 385, 427, 434, 476, 518, 560, 602, 644, 651, 693, 735, 777, 819
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 03 2020
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LINKS
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FORMULA
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Sum_{n>=2} 1/a(n) = 3.03303318... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
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MATHEMATICA
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f[n_, b_] := Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 6], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
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PROG
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(Magma) [n: n in [0..900] | Intseq(n, 6) eq Reverse(Intseq(n, 6))]; // Vincenzo Librandi, Sep 09 2015
(Python)
from gmpy2 import digits
from sympy import integer_log
if n == 1: return 0
y = 6*(x:=6**integer_log(n>>1, 6)[0])
return int((c:=n-x)*x+int(digits(c, 6)[-2::-1]or'0', 6) if n<x+y else (c:=n-y)*y+int(digits(c, 6)[-1::-1]or'0', 6)) # Chai Wah Wu, Jun 14 2024
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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