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%I #23 Jan 06 2020 21:26:28
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,18,20,21,22,24,25,27,28,30,32,
%T 33,35,36,40,42,44,45,48,49,54,55,56,63,64,66,72,77,81,88,99,101,110,
%U 111,121,131,132,141,151,154,161,165,171,176,181,191,198
%N Products of two palindromes in base 10.
%C Geneviève Paquin, p. 5: "Lemma 3.7: a Christoffel word can always be written as the product of two palindromes." Products of two palindromes in base 10 may be either a palindrome (e.g., 202 * 202 = 40804} or a nonpalindrome (e.g., 2 * 88 = 176, or 22 * 33 = 726}. Contains A115683 and A141322 as proper subsets.
%H Robert Israel, <a href="/A140332/b140332.txt">Table of n, a(n) for n = 1..10000</a>
%H Geneviève Paquin, <a href="http://arXiv.org/abs/0805.4174">On a generalization of Christoffel words: epichristoffel words</a>, arXiv:0805.4174 [math.CO], 2008-2009.
%F {i*j such that i is in A002113 and j is in A002113} = A002113 UNION A115683.
%p digrev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end:
%p N:=3:
%p Res:= $0..9:
%p for d from 2 to N do
%p if d::even then
%p m:= d/2;
%p Res:= Res, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);
%p else
%p m:= (d-1)/2;
%p Res:= Res, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);
%p fi
%p od:
%p Palis:= [Res]:
%p Res:= 0:
%p for i from 2 to nops(Palis) while Palis[i]^2 <= 10^N do
%p for j from i to nops(Palis) while Palis[i]*Palis[j] <= 10^N do
%p Res:= Res, Palis[i]*Palis[j];
%p od od:sort(convert({Res},list)); # _Robert Israel_, Jan 06 2020
%t pal = Select[ Range[0, 200], # == FromDigits@ Reverse@ IntegerDigits@ # &]; Select[ Union[ Times @@@ Tuples[pal, 2]], # <= 200 &] (* _Giovanni Resta_, Jun 20 2016 *)
%Y Cf. A002113, A115683, A141322.
%K easy,nonn,base
%O 1,3
%A _Jonathan Vos Post_, May 28 2008
%E Data corrected by _Giovanni Resta_, Jun 20 2016
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