[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A141322
Nonpalindromes which are products of two palindromes in base 10.
3
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
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
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Aug 02 2008
EXTENSIONS
Extended beyond 330 by R. J. Mathar, Aug 09 2008
STATUS
approved