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A140332 Products of two palindromes in base 10.

%I A140332 #27 Sep 29 2024 21:10:14
%S A140332 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 A140332 33,35,36,40,42,44,45,48,49,54,55,56,63,64,66,72,77,81,88,99,101,110,
%U A140332 111,121,131,132,141,151,154,161,165,171,176,181,191,198
%N A140332 Products of two palindromes in base 10.
%C A140332 Geneviève Paquin, p. 5: "Lemma 3.7: a Christoffel word can always be written as the product of two palindromes."
%C A140332 Contains A115683 and A141322 as proper subsets.
%H A140332 Robert Israel, <a href="/A140332/b140332.txt">Table of n, a(n) for n = 1..10000</a>
%H A140332 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 A140332 A002113 UNION A115683.
%p A140332 digrev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end:
%p A140332 N:=3:
%p A140332 Res:= $0..9:
%p A140332 for d from 2 to N do
%p A140332   if d::even then
%p A140332     m:= d/2;
%p A140332     Res:= Res, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);
%p A140332   else
%p A140332     m:= (d-1)/2;
%p A140332     Res:= Res, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);
%p A140332   fi
%p A140332 od:
%p A140332 Palis:= [Res]:
%p A140332 Res:= 0:
%p A140332 for i from 2 to nops(Palis) while Palis[i]^2 <= 10^N do
%p A140332   for j from i to nops(Palis) while Palis[i]*Palis[j] <= 10^N do
%p A140332      Res:= Res, Palis[i]*Palis[j];
%p A140332 od od:sort(convert({Res},list)); # _Robert Israel_, Jan 06 2020
%t A140332 pal = Select[ Range[0, 200], # == FromDigits@ Reverse@ IntegerDigits@ # &]; Select[ Union[ Times @@@ Tuples[pal, 2]], # <= 200 &] (* _Giovanni Resta_, Jun 20 2016 *)
%Y A140332 Cf. A002113, A115683, A141322.
%K A140332 easy,nonn,base
%O A140332 1,3
%A A140332 _Jonathan Vos Post_, May 28 2008
%E A140332 Data corrected by _Giovanni Resta_, Jun 20 2016