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

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

Author

Amarnath Murthy, Jul 05 2001

Keywords

• nonn
• base
• easy

Examples

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

Links

• 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.

Crossrefs

Cf. A048343, A048344.

Programs

Mathematica

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 *)

PARI

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

Python

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

Formula

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

Extensions

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