

A357314


a(1) = 1; a(n) is the second smallest number k such that k > a(n1) and concatenation of a(1), ..., a(n1), k is a palindrome.


0



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

1,2


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.


LINKS



EXAMPLE

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.


PROG

(Python)
pal = lambda s: s == s[::1]
up_to = 10
terms = [1, ]
for i in range(up_to1):
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)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



