

A166749


Numbers that are the sum or product of two numbers, such that the sum and product have reversed digits.


1



0, 4, 18, 27, 49, 72, 81, 94, 499, 994, 4999, 9994, 49999, 99994, 499999, 999994, 4999999, 9999994, 49999999, 99999994, 499999999, 999999994, 4999999999, 9999999994, 49999999999, 99999999994, 499999999999, 999999999994, 4999999999999, 9999999999994, 49999999999999
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OFFSET

1,2


COMMENTS

Note that 0 and 4 are their own reverseddigit 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 casebycase analysis.  Wang Pok Lo, Dec 24 2018


LINKS

Table of n, a(n) for n=1..31.
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

Sequence in context: A099565 A063563 A323848 * A103067 A080519 A120407
Adjacent sequences: A166746 A166747 A166748 * A166750 A166751 A166752


KEYWORD

nonn,base,easy


AUTHOR

Mark Nandor, Oct 21 2009


STATUS

approved



