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A140332 Products of two palindromes in base 10. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

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.

FORMULA

{i*j such that i is in A002113 and j is in A002113} = A002113 UNION A115683.

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 *)

CROSSREFS

Cf. A002113, A115683, A141322.

Sequence in context: A084034 A084347 A051038 * A155182 A096076 A108864

Adjacent sequences:  A140329 A140330 A140331 * A140333 A140334 A140335

KEYWORD

easy,nonn,base

AUTHOR

Jonathan Vos Post, May 28 2008

EXTENSIONS

Data corrected by Giovanni Resta, Jun 20 2016

STATUS

approved

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Last modified May 16 11:33 EDT 2021. Contains 343942 sequences. (Running on oeis4.)