A322835 Non-palindromic numbers n such that n * reverse(n) is a square and n and reverse(n) do not have the same number of digits.

100, 200, 300, 400, 500, 600, 700, 800, 900, 1100, 2200, 3300, 4400, 5500, 6600, 7700, 8800, 9900, 10000, 10100, 11100, 12100, 13100, 14100, 14400, 15100, 16100, 16900, 17100, 18100, 19100, 20000, 20200, 21200, 22200, 23200, 24200, 25200, 26200, 27200, 28200, 28800, 29200, 30000, 30300

Offset

1,1

Comments

The terms in this sequence are mostly of the form m * 100^k with k >= 1, but this condition is not sufficient.

A062917 U {this sequence} = A070760, with empty intersection.

There are exactly four families of such integers here: numbers of the forms A002113(j)*100^k, A035090(j)*100^k, A082994(j)*100^k and A323061(j)*10^(2k+1).

All terms are multiples of 10, but they are not necessarily multiples of 100. The first multiple of 10 that is not a multiple of 100 is a(755) = 5449680, and there are only 30 such terms among the first 10000 terms. - Chai Wah Wu, Jan 07 2019

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

Example for family 1: 200 * 2 = 400 = 20^2;
Example for family 2: 14400 * 441 = 120^2 * 21^2 = 2520^2;
Example for family 3: 28800 * 882 = (2 * 120^2) * (2 * 21^2) = 5040^2.
Example for family 4: 5449680 * 869445 = 2176740^2. - Chai Wah Wu, Jan 07 2019

Mathematica

Select[100 Range@303, And[! PalindromeQ@ #, IntegerQ@ Sqrt[#1 #2], UnsameQ @@ IntegerLength@ {#1, #2}] & @@ {#, IntegerReverse@ #} &] (* Michael De Vlieger, Jan 03 2019 *)

Prog

(PARI) is(n) = n % 10 == 0 && issquare(n * fromdigits(Vecrev(digits(n)))) \\ David A. Corneth, Jan 03 2019

Crossrefs

Cf. A002113, A004086, A035090, A062917, A070760, A082994, A323061.

Sequence in context: A043490 A218037 A044713 * A031498 A053402 A181568

Adjacent sequences: A322832 A322833 A322834 * A322836 A322837 A322838

Keyword

nonn,base

Author

Bernard Schott, Jan 02 2019

Status

approved