A029730 - OEIS

%I #42 Jun 14 2024 01:49:45

%S 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,

%T 170,187,204,221,238,255,257,273,289,305,321,337,353,369,385,401,417,

%U 433,449,465,481,497,514,530,546,562,578,594,610,626,642

%N Numbers that are palindromic in base 16.

%H Reinhard Zumkeller, <a href="/A029730/b029730.txt">Table of n, a(n) for n = 1..10000</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>.

%H Phakhinkon Phunphayap and Prapanpong Pongsriiam, <a href="https://doi.org/10.13140/RG.2.2.23202.79047">Estimates for the Reciprocal Sum of b-adic Palindromes</a>, 2019.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>.

%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Palindromic_number">Palindromic number</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hexadecimal">Hexadecimal</a>.

%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>

%F Sum_{n>=2} 1/a(n) = 3.71109616... (Phunphayap and Pongsriiam, 2019). - _Amiram Eldar_, Oct 17 2020

%e 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

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

%o (Haskell)

%o a029730 n = a029730_list !! (n-1)

%o a029730_list = map (foldr (\h v -> 16 * v + h) 0) $

%o                    filter (\xs -> xs == reverse xs) a262437_tabf

%o -- _Reinhard Zumkeller_, Sep 23 2015

%o (PARI) isok(n) = my(v=digits(n,16)); v == Vecrev(v); \\ _Michel Marcus_, Sep 30 2018

%o (Python)

%o def A029730(n):

%o     if n == 1: return 0

%o     y = (x:=1<<(n.bit_length()-2&-4))<<4

%o     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

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

%K nonn,base

%O 1,3

%A _Patrick De Geest_