cp's OEIS Frontend

A343524 Palindromes with digits strictly increasing up to the middle digit.

%I A343524 #29 Apr 25 2021 13:10:07
%S A343524 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,121,131,141,151,161,
%T A343524 171,181,191,232,242,252,262,272,282,292,343,353,363,373,383,393,454,
%U A343524 464,474,484,494,565,575,585,595,676,686,696,787,797,898,1221,1331
%N A343524 Palindromes with digits strictly increasing up to the middle digit.
%C A343524 The maximum term in the sequence is 123456789987654321, if leading zeros are not allowed.
%H A343524 Michael S. Branicky, <a href="/A343524/b343524.txt">Table of n, a(n) for n = 1..1023</a>
%e A343524 121 and 1221 are legal terms but 122221 is not, since the digits 2,2 at positions 2 and 3 are not increasing.
%o A343524 (Perl)
%o A343524 #!/usr/bin/perl
%o A343524 open(OUT,">incrDecrPalindrome.txt")||die "open fail OUT\n";
%o A343524 foreach $cand (0..100000){
%o A343524     @a=split("",$cand);
%o A343524     $b = join("",reverse @a);
%o A343524     next unless $cand==$b; # palindromes only
%o A343524     $n = int(@a/2.);
%o A343524     $n-- if &is_even(0+@a); # backoff if even count of digits
%o A343524     foreach $i (1..$n){
%o A343524         goto skip_num unless $a[$i-1] < $a[$i];
%o A343524     }
%o A343524     print OUT "$cand,";
%o A343524 skip_num:;
%o A343524     print "";
%o A343524 }
%o A343524 print OUT "\n";
%o A343524 ##########################################
%o A343524 sub is_even{  $_[0]/2. == int $_[0]/2.  }
%o A343524 ##########################################
%o A343524 (Python)
%o A343524 from itertools import combinations
%o A343524 A343524_list = [0]
%o A343524 for l in range(1,4):
%o A343524     for d in combinations('123456789',l):
%o A343524         s = ''.join(d)
%o A343524         A343524_list.append(int(s+s[-2::-1]))
%o A343524     for d in combinations('123456789',l):
%o A343524         s = ''.join(d)
%o A343524         A343524_list.append(int(s+s[::-1])) # _Chai Wah Wu_, Apr 24 2021
%Y A343524 Cf. A002113, A009993, A062351 (primes), A134941.
%K A343524 nonn,base,fini,full
%O A343524 1,3
%A A343524 _James S. DeArmon_, Apr 18 2021
%E A343524 Terms < 100 prepended by _Rémy Sigrist_, Apr 25 2021