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 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

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