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

1,2

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.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A048343, A048344.

Sequence in context: A060812 A212129 A172409 * A136972 A227764 A135115

Adjacent sequences: A062933 A062934 A062935 * A062937 A062938 A062939

Keyword

nonn,base,easy

Author

Amarnath Murthy, Jul 05 2001

Extensions

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

Status

approved