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A029730
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Numbers that are palindromic in base 16.
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10
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 257, 273, 289, 305, 321, 337, 353, 369, 385, 401, 417, 433, 449, 465, 481, 497, 514, 530, 546, 562, 578, 594, 610, 626, 642
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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Sum_{n>=2} 1/a(n) = 3.71109616... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
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EXAMPLE
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 11, 22, 33, 44, 55, 66, 77, 88, 99, AA, BB, CC, DD, EE, FF, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191,1A1, 1B1, 1C1, 1D1, 1E1, 1F1, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 2A2, 2B2, 2C2, 2D2, 2E2, 2F2, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 3A3, 3B3, 3C3, 3D3, 3E3, 3F3, 404, ... - Reinhard Zumkeller, Sep 23 2015
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MATHEMATICA
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palindromicQ[n_, b_] := Module[{i = IntegerDigits[n, b]}, i == Reverse[i]]; Select[Range[1000], palindromicQ[#, 16] &] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
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PROG
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(Haskell)
a029730 n = a029730_list !! (n-1)
a029730_list = map (foldr (\h v -> 16 * v + h) 0) $
filter (\xs -> xs == reverse xs) a262437_tabf
(PARI) isok(n) = my(v=digits(n, 16)); v == Vecrev(v); \\ Michel Marcus, Sep 30 2018
(Python)
if n == 1: return 0
y = (x:=1<<(n.bit_length()-2&-4))<<4
return (c:=n-x)*x+int(hex(c)[-2:1:-1]or'0', 16) if n<x+y else (c:=n-y)*y+int(hex(c)[-1:1:-1]or'0', 16) # Chai Wah Wu, Jun 13 2024
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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