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A029957
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Numbers that are palindromic in base 12.
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10
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 145, 157, 169, 181, 193, 205, 217, 229, 241, 253, 265, 277, 290, 302, 314, 326, 338, 350, 362, 374, 386, 398, 410, 422, 435, 447, 459, 471, 483, 495, 507, 519, 531
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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 04 2020
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LINKS
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FORMULA
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Sum_{n>=2} 1/a(n) = 3.4989489... (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, 12], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
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PROG
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(PARI) isok(n) = my(d=digits(n, 12)); d == Vecrev(d); \\ Michel Marcus, May 13 2017
(Python)
from sympy import integer_log
from gmpy2 import digits
if n == 1: return 0
y = 12*(x:=12**integer_log(n>>1, 12)[0])
return int((c:=n-x)*x+int(digits(c, 12)[-2::-1]or'0', 12) if n<x+y else (c:=n-y)*y+int(digits(c, 12)[-1::-1]or'0', 12)) # 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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