A141322 Nonpalindromes which are products of two palindromes in base 10.

10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72, 81, 110, 132, 154, 165, 176, 198, 220, 231, 264, 275, 297, 302, 308, 322, 330, 342, 352, 362, 382, 385, 396, 423, 440, 453, 462, 483, 495, 504, 513, 524, 528

Offset: 1

Author

Jonathan Vos Post, Aug 02 2008

Keywords

• base
• easy
• nonn

Examples

			726 is in this sequence because 22 * 33 = 726, 22 and 33 are palindromes base 10, but 726 is not a palindrome base 10.
		

Links

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

Crossrefs

Cf. A002113, A004086, A140332.

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: # for terms of at most N digits
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:= NULL:
for i from 3 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
     v:= Palis[i]*Palis[j];      if digrev(v) <> v then Res:= Res, v fi;
od od:sort(convert({Res},list)); # Robert Israel, Jan 06 2020

Formula

{A140332 INTERSECTION COMPLEMENT(A002113)} = {n in A115683 and n <> A004086(n)}.

Extensions

Extended beyond 330 by R. J. Mathar, Aug 09 2008