

A322835


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


6



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
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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



