A166749 Numbers that are the sum or product of two numbers, such that the sum and product have reversed digits.

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

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

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: A063563 A323848 A358375 * A370406 A103067 A080519

Adjacent sequences: A166746 A166747 A166748 * A166750 A166751 A166752

Keyword

nonn,base,easy

Author

Mark Nandor, Oct 21 2009

Status

approved