A141322 -id:A141322 - cp's OEIS frontend

A115683 Numbers that are the product of 2 palindromes greater than 1.

4, 6, 8, 9, 10, 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, 110, 121, 132, 154, 165, 176, 198, 202, 220, 222, 231, 242, 262, 264, 275, 282, 297, 302, 303, 308, 322, 330, 333

Offset: 1

Giovanni Resta, Jan 31 2006

			262 = 2 * 131.
264 = 6 * 11.
275 = 5 * 55.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A002113, A141322.

revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
N:=4; # to get terms <= 2*10^N
Pals:= $2..9:
for d from 2 to N do
  if d::even then
    m:= d/2;
    Pals:= Pals, seq(n*10^m + revdigs(n), n=10^(m-1)..10^m-1);
  else
    m:= (d-1)/2;
    Pals:= Pals, seq(seq(n*10^(m+1)+y*10^m+revdigs(n), y=0..9), n=10^(m-1)..10^m-1);
  fi
od:
Pals:= {Pals}: nP:= nops(Pals):
P2:= select(`<`,{seq(seq(Pals[i]*Pals[j],j=1..i),i=1..nP)},2*10^N):
sort(convert(P2,list)); # Robert Israel, Mar 16 2020

pal = Select[ Range[2, 400], # == FromDigits@ Reverse@ IntegerDigits@ # &]; Select[Union[Times @@@ Tuples[pal, 2]], # <= 400 &] (* Giovanni Resta, Jun 20 2016 *)

A140332 Products of two palindromes in base 10.

Original entry on oeis.org

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

Jonathan Vos Post, May 28 2008

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.

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.

Cf. A002113, A115683, A141322.

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

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

A002113 UNION A115683.

Data corrected by Giovanni Resta, Jun 20 2016

cp's OEIS Frontend

A115683 Numbers that are the product of 2 palindromes greater than 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica