OFFSET
1,1
COMMENTS
These numbers are counterexamples to the following conjecture given in the Ogilvy-Anderson reference: "When an integer and its reversal are unequal, their product is never a square except when both are squares." This sequence excludes terms like 2200, i.e. 2200*22 = 48400.
Contains x*(10^k+1) for k >= 3 with x in {144, 169, 288, 441, 528, 768, 825, 867, 882, 961}. - Robert Israel, Jun 11 2018
REFERENCES
C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, NY. (1966), pp. 88-89.
J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 82-83. ASIN: B002ACVZ6O [From Jason Earls, Nov 22 2009]
LINKS
Robert Israel, Table of n, a(n) for n = 1..168
M. A. Rashid, M. A. Uppal, D. C. B. Marsh and A. Wayne, Product of a Number and Its Reverse, American Mathematical Monthly, vol. 64 (1957), p. 434, E-1243. - Felix Fröhlich, Jul 11 2014
EXAMPLE
a(5) = 867 because 867 * 768 = 665856 = 816^2.
MAPLE
revdigs:= proc(n) local L;
L:= convert(n, base, 10);
add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
filter:= proc(n) local r;
if issqr(n) then return false fi;
r:= revdigs(n);
r <> n and issqr(r*n) and not issqr(r);
end proc:
select(filter, [seq(seq(10*i+j, j=1..9), i=1..10^4)]); # Robert Israel, Jun 11 2018
MATHEMATICA
Select[Range[10^5], And[UnsameQ @@ {#1, #2}, IntegerQ@ Sqrt[#1 #2], AllTrue[{#1, #2}, ! IntegerQ@ Sqrt@ # &], SameQ @@ (IntegerLength@ {#1, #2})] & @@ {#, IntegerReverse@ #} &] (* Michael De Vlieger, Jan 04 2019 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Jason Earls, May 29 2003
EXTENSIONS
Name clarified by Bernard Schott, Jan 04 2019
STATUS
approved