A140332 Products of two palindromes in base 10.

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, 33, 35, 36, 40, 42, 44, 45, 48, 49, 54, 55, 56, 63, 64, 66, 72, 77, 81, 88, 99, 101, 110, 111, 121, 131, 132, 141, 151, 154, 161, 165, 171, 176, 181, 191, 198

Offset: 1

Author

Jonathan Vos Post, May 28 2008

Keywords

• easy
• nonn
• base

Comments

Geneviève Paquin, p. 5: "Lemma 3.7: a Christoffel word can always be written as the product of two palindromes."

Contains A115683 and A141322 as proper subsets.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Geneviève Paquin, On a generalization of Christoffel words: epichristoffel words, arXiv:0805.4174 [math.CO], 2008-2009.

Crossrefs

Cf. A002113, A115683, A141322.

Programs

Maple

digrev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end:
N:=3:
Res:= $0..9:
for d from 2 to N do
  if d::even then
    m:= d/2;
    Res:= Res, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);
  else
    m:= (d-1)/2;
    Res:= Res, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);
  fi
od:
Palis:= [Res]:
Res:= 0:
for i from 2 to nops(Palis) while Palis[i]^2 <= 10^N do
  for j from i to nops(Palis) while Palis[i]*Palis[j] <= 10^N do
     Res:= Res, Palis[i]*Palis[j];
od od:sort(convert({Res},list)); # Robert Israel, Jan 06 2020

Mathematica

pal = Select[ Range[0, 200], # == FromDigits@ Reverse@ IntegerDigits@ # &]; Select[ Union[ Times @@@ Tuples[pal, 2]], # <= 200 &] (* Giovanni Resta, Jun 20 2016 *)

Formula

A002113 UNION A115683.

Extensions

Data corrected by Giovanni Resta, Jun 20 2016