OFFSET
1,2
COMMENTS
Note that 0 and 4 are their own reversed-digit sums and products, since 0+0=0*0=0 and 2+2=2*2=4. The pattern of some number of nines and then a four, and a four and some number of nines, continues indefinitely.
These are in fact all the solutions, shown by a case-by-case analysis. - Wang Pok Lo, Dec 24 2018
LINKS
W. P. Lo and Y. Paz, On finding all positive integers a,b such that b±a and ab are palindromic, arXiv:1812.08807 [math.HO] (2018).
FORMULA
For n>8, a(n)=5*10^((n+1)/2 - 3) - 1 if n odd; a(n)=10^(n/2 - 2) - 6 if n even.
EXAMPLE
For instance, 9*9=81 and 9+9=18 are terms; 3*24=72 and 3+24=27 are terms too.
MATHEMATICA
Do[If[IntegerDigits[x y] == Reverse[IntegerDigits[x + y]], Print[{x, y, x + y, x y}]], {x, 0, 20}, {y, x, 100000}] or a[1]=0; a[2]=4; a[3]=18; a[4]=27; a[5]=49; a[6]=72; a[7]=81; a[8]=94 a[n_] := a[n] = If[OddQ[n], 5*10^((n + 1)/2 - 3) - 1, 10^(n/2 - 2) - 6]
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Mark Nandor, Oct 21 2009
STATUS
approved