login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A343524 Palindromes with digits strictly increasing up to the middle digit. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

EXAMPLE

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

PROG

(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

CROSSREFS

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

Sequence in context: A082810 A344550 A010785 * A032573 A190217 A222620

Adjacent sequences:  A343521 A343522 A343523 * A343525 A343526 A343527

KEYWORD

nonn,base,fini,full

AUTHOR

James S. DeArmon, Apr 18 2021

EXTENSIONS

Terms < 100 prepended by Rémy Sigrist, Apr 25 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)