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

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 121, 131, 141, 151, 161, 171, 181, 191, 232, 242, 252, 262, 272, 282, 292, 343, 353, 363, 373, 383, 393, 454, 464, 474, 484, 494, 565, 575, 585, 595, 676, 686, 696, 787, 797, 898, 1221, 1331

Offset: 1

Author

James S. DeArmon, Apr 18 2021

Keywords

• nonn
• base
• fini
• full

Comments

The maximum term in the sequence is 123456789987654321, if leading zeros are not allowed.

Examples

			121 and 1221 are legal terms but 122221 is not, since the digits 2,2 at positions 2 and 3 are not increasing.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1023

Crossrefs

Cf. A002113, A009993, A062351 (primes), A134941.

Programs

Perl

#!/usr/bin/perl
open(OUT,">incrDecrPalindrome.txt")||die "open fail OUT\n";
foreach $cand (0..100000){
    @a=split("",$cand);
    $b = join("",reverse @a);
    next unless $cand==$b; # palindromes only
    $n = int(@a/2.);
    $n-- if &is_even(0+@a); # backoff if even count of digits
    foreach $i (1..$n){
        goto skip_num unless $a[$i-1] < $a[$i];
    }
    print OUT "$cand,";
skip_num:;
    print "";
}
print OUT "\n";
##########################################
sub is_even{  $[0]/2. == int $[0]/2.  }
##########################################

Python

from itertools import combinations
A343524_list = [0]
for l in range(1,4):
    for d in combinations('123456789',l):
        s = ''.join(d)
        A343524_list.append(int(s+s[-2::-1]))
    for d in combinations('123456789',l):
        s = ''.join(d)
        A343524_list.append(int(s+s[::-1])) # Chai Wah Wu, Apr 24 2021

Extensions

Terms < 100 prepended by Rémy Sigrist, Apr 25 2021