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 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. 0
 1, 21, 1121, 1211121, 2111211211121, 112112111212111211211121, 12111212111211211121112112111212111211211121, 211121121112111211211121211121121112112111212111211211121112112111212111211211121 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..8. 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_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) CROSSREFS Cf. A000073, A002275, A055642, A083122, A305393. Sequence in context: A193156 A012183 A012230 * A270505 A086098 A086875 Adjacent sequences: A357311 A357312 A357313 * A357315 A357316 A357317 KEYWORD nonn,base AUTHOR Gleb Ivanov, Sep 23 2022 STATUS approved

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Last modified May 20 11:25 EDT 2024. Contains 372712 sequences. (Running on oeis4.)