A029742 Nonpalindromic numbers.

10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 102, 103, 104, 105, 106, 107

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• easy
• nice

Comments

Complement of A002113; A136522(a(n)) = 0.

A064834(a(n)) > 0. - Reinhard Zumkeller, Sep 18 2013

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Patrick De Geest, World!Of Numbers
• Index entries for sequences related to palindromes

Crossrefs

Cf. A002113. Different from A031955.

Programs

Haskell

a029742 n = a029742_list !! (n-1)
a029742_list = filter ((== 0) . a136522) [1..]
-- Reinhard Zumkeller, Oct 09 2011

Magma

[n: n in [0..150] | Intseq(n) ne Reverse(Intseq(n))]; // Bruno Berselli, Apr 01 2015

Mathematica

palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; DeleteCases[ Range[10,110],?palQ] (* _Harvey P. Dale, Jan 28 2012 *)
Table[If[PalindromeQ[n],Nothing,n],{n,120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 13 2019 *)

PARI

is(n)=my(d=digits(n)); d!=Vecrev(d) \\ Charles R Greathouse IV, Feb 06 2017

Python

def ok(n): s = str(n); return s != s[::-1]
print(list(filter(ok, range(108)))) # Michael S. Branicky, Oct 12 2021

Python

def A029742(n):
    def f(x): return n+x//10**((l:=len(s:=str(x)))-(k:=l+1>>1))-(int(s[k-1::-1])>x%10**k)+10**(k-1+(l&1^1))-1
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m # Chai Wah Wu, Jul 24 2024

Extensions

Offset corrected by Reinhard Zumkeller, Oct 09 2011