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

1,1

Links

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

Formula

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

Example

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

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

Crossrefs

Cf. A002113, A004086, A140332.

Sequence in context: A199991 A161598 A122426 * A350180 A099103 A208271

Adjacent sequences: A141319 A141320 A141321 * A141323 A141324 A141325

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Aug 02 2008

Extensions

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

Status

approved