A029730 Numbers that are palindromic in base 16.

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

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.

Index entries for sequences related to palindromes

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

Cf. A029731 (also palindromic in decimal), A056962, A262437.

Sequence in context: A048313 A043719 A296759 * A297289 A048327 A048340

Adjacent sequences: A029727 A029728 A029729 * A029731 A029732 A029733

Keyword

nonn,base

Author

Patrick De Geest

Status

approved