A266139 - OEIS

%I #12 Aug 22 2021 00:15:46

%S 0,1,2,3,4,5,6,7,8,9,101,202,212,303,313,323,404,414,424,434,505,515,

%T 525,535,545,606,616,626,636,646,656,707,717,727,737,747,757,767,808,

%U 818,828,838,848,858,868,878,909,919,929,939,949,959,969,979,989,11011

%N Volcano palindromes: palindromes not in A110784 such that removing one digit will result in a term in A110784.

%C All terms have odd number of digits. Terms are palindromes such that digits are nondecreasing halfway through except for the middle digit, which is strictly smaller than its neighboring digits.

%C Illustration using a term of this sequence, 23446564432:

%C .  .  .  .  6  .  6  .  .  .  .

%C .  .  .  .  .  5  .  .  .  .  .

%C .  .  4  4  .  .  .  4  4  .  .

%C .  3  .  .  .  .  .  .  .  3  .

%C 2  .  .  .  .  .  .  .  .  .  2

%H Chai Wah Wu, <a href="/A266139/b266139.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o from itertools import combinations_with_replacement as mc

%o def agentod(digits):

%o     yield from range(10)

%o     for d in range(3, digits+1, 2):

%o         for left in mc("123456789", d//2):

%o             for center in range(int(left[-1])):

%o                 yield int("".join(left + (str(center), ) + left[::-1]))

%o print([an for an in agentod(5)]) # _Michael S. Branicky_, Aug 21 2021

%Y Cf. A110784.

%K nonn,easy,base

%O 1,3

%A _Chai Wah Wu_, Dec 25 2015