A048344 -id:A048344 - cp's OEIS frontend

A048343 Total number of distinct palindromes of form 'n-digit number' x 'n-digit number_reversed' (n-digit number not palindromic).

0, 1, 3, 10, 19, 44, 86, 171, 308, 551, 920

Offset: 1

Patrick De Geest, Feb 15 1999

			E.g., 3 solutions for 3-digit numbers: 102 * 201 = 20502; 112 * 211 = 23632; 122 * 221 = 26962.

P. De Geest, Palindromic Products of Non Palindromic Integers and their Reversals

Cf. A048344.

def A048343(n):
    y, plist = 0, []
    for i in range(10**(n-1),10**n):
        s1 = str(i)
        s2 = s1[::-1]
        if s1 != s2:
            p = i*int(s2)
            if not p in plist:
                sp = str(p)
                if sp == sp[::-1]:
                    plist.append(p)
                    y += 1
    return y # Chai Wah Wu, Sep 05 2014

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 18 2006

Offset changed and two terms added by Lars Blomberg, Nov 25 2011

A062936 Numbers n such that n*R(n) is a palindrome, where R(n) (A004086) = digit reversal.

Original entry on oeis.org

1, 2, 3, 11, 12, 21, 22, 101, 102, 111, 112, 121, 122, 201, 202, 211, 212, 221, 1001, 1002, 1011, 1012, 1021, 1022, 1101, 1102, 1111, 1112, 1121, 1201, 1202, 1211, 2001, 2002, 2011, 2012, 2021, 2101, 2102, 2111, 2201, 10001, 10002, 10011, 10012

Offset: 1

Amarnath Murthy, Jul 05 2001

			122*221 = 26962 hence 122 belongs to the sequence.

Harry J. Smith and Indranil Ghosh, Table of n, a(n) for n = 1..4357 (first 500 terms from Harry J. Smith)
Martianus Frederic Ezerman, Bertrand Meyer and Patrick Solé, On Polynomial Pairs of Integers, arXiv:1210.7593 [math.NT], 2012. - From _N. J. A. Sloane_, Nov 08 2012
Martianus Frederic Ezerman, Bertrand Meyer and Patrick Solé, On Polynomial Pairs of Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.5.

Cf. A048343, A048344.

Select[Range[100000], Reverse[IntegerDigits[ #*FromDigits[Reverse[IntegerDigits[ # ]]]]] == IntegerDigits[ #*FromDigits[Reverse[IntegerDigits[ # ]]]] &] (* Tanya Khovanova, Jun 17 2009 *)
Select[Range[11000],PalindromeQ[# IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 21 2020 *)

lista(nn) = for(n=1, nn, my(d=digits(n*eval(concat(Vecrev(Str(n)))), 10)); if(d == Vecrev(d), print1(n, ", "))); \\ Altug Alkan, Mar 26 2016

A062936_list = []
for n in range(1,10**5):
    s = str(n*int(str(n)[::-1]))
    if s == s[::-1]:
        A062936_list.append(n) # Chai Wah Wu, Sep 08 2014

Includes integers not ending in 0 with sum of squares of digits < 10. - David W. Wilson, Jul 06 2001

Corrected and extended by Dean Hickerson and Patrick De Geest, Jul 06 2001

cp's OEIS Frontend

A048343 Total number of distinct palindromes of form 'n-digit number' x 'n-digit number_reversed' (n-digit number not palindromic).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

Extensions