A357314 a(1) = 1; a(n) is the second smallest number k such that k > a(n-1) and concatenation of a(1), ..., a(n-1), k is a palindrome.

1, 21, 1121, 1211121, 2111211211121, 112112111212111211211121, 12111212111211211121112112111212111211211121, 211121121112111211211121211121121112112111212111211211121112112111212111211211121

Offset: 1

Author

Gleb Ivanov, Sep 23 2022

Keywords

• nonn
• base

Comments

Conjecture: Length A055642(a(n)) = A000073(n+2), and A305393 is a sequence of digits in the concatenation of all terms in this sequence.

Examples

			For n = 3 concatenation of the previous terms is 121. Numbers that would make it a palindrome if concatenated to it are 121, 1121, ... and the second smallest of them is a(3) = 1121.
		

Crossrefs

Cf. A000073, A002275, A055642, A083122, A305393.

Programs

Python

pal = lambda s: s == s[::-1]
up_to = 10
terms = [1, ]
for i in range(up_to-1):
    c, r = ''.join(map(str, terms)), 0
    for j in range(len(str(terms[-1])), len(c)+1):
        found, p  = False, int(c[:j][::-1])
        if p > terms[-1] and pal(c + c[:j][::-1]):
            r+=1
            if r == 2:
                terms.append(p);found = True;break
    if found: continue
    j = 0
    while 1:
        j+=1
        r+=1
        if r == 2:
            terms.append(int(str(j) + c[::-1]))
            break
print(terms)