A061917 Either a palindrome or becomes a palindrome if trailing 0's are omitted.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 110, 111, 121, 131, 141, 151, 161, 171, 181, 191, 200, 202, 212, 220, 222, 232, 242, 252, 262, 272, 282, 292, 300, 303, 313, 323, 330, 333, 343, 353, 363, 373, 383, 393, 400, 404

Offset: 1

Author

N. J. A. Sloane, Jun 27 2001

Keywords

• nonn
• base
• easy
• nice

Comments

Numbers that are palindromes when written with a suitable number of leading zeros. - Jeppe Stig Nielsen, Jan 17 2022

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113, A057890, A057891.

Programs

Haskell

a061917 n = a061917_list !! (n-1)
a061917_list = filter chi [0..] where
   chi x = zs == reverse zs where
      zs = dropWhile (== '0') $ reverse $ show x
-- Reinhard Zumkeller, Sep 25 2011

Mathematica

PaleQ[n_Integer, base_Integer] := Module[{idn, trim = n/base^IntegerExponent[n, base]}, idn = IntegerDigits[trim, base]; idn == Reverse[idn]]; Select[Range[0, 500], PaleQ[#, 10] &] (* Lei Zhou, Dec 13 2013 *)
Join[{0},Select[Range[500],PalindromeQ[FromDigits[Drop[IntegerDigits[#],-IntegerExponent[#,10]]]]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 27 2017 *)

PARI

isOK(k)=k==0||fromdigits(Vecrev(digits(k)))==k/10^valuation(k,10) \\ Jeppe Stig Nielsen, Jan 17 2022

Python

def ispal(s): return s == s[::-1]
def ok(n): s = str(n); return ispal(s) or ispal(s.rstrip('0'))
print([k for k in range(405) if ok(k)]) # Michael S. Branicky, Jan 17 2022

Formula

A136522(A004151(a(n))) = 1. - Reinhard Zumkeller, Sep 25 2011

Extensions

Corrected by Ray Chandler, Jun 08 2009