OFFSET
1,3
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Patrick De Geest, Palindromic numbers beyond base 10.
Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019.
Eric Weisstein's World of Mathematics, Palindromic Number.
Eric Weisstein's World of Mathematics, Hexadecimal.
Wikipedia, Palindromic number.
Wikipedia, Hexadecimal.
FORMULA
Sum_{n>=2} 1/a(n) = 3.71109616... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
EXAMPLE
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
MATHEMATICA
palindromicQ[n_, b_] := Module[{i = IntegerDigits[n, b]}, i == Reverse[i]]; Select[Range[1000], palindromicQ[#, 16] &] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
PROG
(Haskell)
a029730 n = a029730_list !! (n-1)
a029730_list = map (foldr (\h v -> 16 * v + h) 0) $
filter (\xs -> xs == reverse xs) a262437_tabf
-- Reinhard Zumkeller, Sep 23 2015
(PARI) isok(n) = my(v=digits(n, 16)); v == Vecrev(v); \\ Michel Marcus, Sep 30 2018
(Python)
def A029730(n):
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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
STATUS
approved