cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A166749 #12 Dec 29 2018 03:55:55
%S A166749 0,4,18,27,49,72,81,94,499,994,4999,9994,49999,99994,499999,999994,
%T A166749 4999999,9999994,49999999,99999994,499999999,999999994,4999999999,
%U A166749 9999999994,49999999999,99999999994,499999999999,999999999994,4999999999999,9999999999994,49999999999999
%N A166749 Numbers that are the sum or product of two numbers, such that the sum and product have reversed digits.
%C A166749 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.
%C A166749 These are in fact all the solutions, shown by a case-by-case analysis. - _Wang Pok Lo_, Dec 24 2018
%H A166749 W. P. Lo and Y. Paz, <a href="https://arxiv.org/abs/1812.08807">On finding all positive integers a,b such that b±a and ab are palindromic</a>, arXiv:1812.08807 [math.HO] (2018).
%F A166749 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.
%e A166749 For instance, 9*9=81 and 9+9=18 are terms; 3*24=72 and 3+24=27 are terms too.
%t A166749 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]
%K A166749 nonn,base,easy
%O A166749 1,2
%A A166749 _Mark Nandor_, Oct 21 2009