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

Author

Patrick De Geest

Keywords

• nonn
• base

Examples

			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
		

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

Crossrefs

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

Programs

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

Mathematica

palindromicQ[n_, b_] := Module[{i = IntegerDigits[n, b]}, i == Reverse[i]]; Select[Range[1000], palindromicQ[#, 16] &] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)

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 nChai Wah Wu, Jun 13 2024

Formula

Sum_{n>=2} 1/a(n) = 3.71109616... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020