cp's OEIS Frontend

A083122 a(1) = 1, then the smallest number not included earlier and not a string of 1's such that the concatenation a(n), a(n+1) is a palindrome.

%I A083122 #16 Aug 10 2022 07:40:05
%S A083122 1,21,2,12,121,1121,211,112,1211,11121,2111,1112,12111,111121,21111,
%T A083122 11112,121111,1111121,211111,111112,1211111,11111121,2111111,1111112,
%U A083122 12111111,111111121,21111111,11111112,121111111,1111111121,211111111,111111112,1211111111
%N A083122 a(1) = 1, then the smallest number not included earlier and not a string of 1's such that the concatenation a(n), a(n+1) is a palindrome.
%C A083122 Starting with a(7), follows the pattern 21^k, 1^k2, 121^k, 1^(k+1)21, 2(1)^(k+1), ..., for k >= 2, where ^ represents repeated concatenation. - _Michael S. Branicky_, Aug 09 2022
%o A083122 (Python)
%o A083122 from itertools import count, islice, product
%o A083122 def pals(digs):
%o A083122     yield from digs
%o A083122     for d in count(2):
%o A083122         for p in product(digs, repeat=d//2):
%o A083122             left = "".join(p)
%o A083122             for mid in [[""], digs][d%2]:
%o A083122                 yield left + mid + left[::-1]
%o A083122 def folds(s): # generator of suffixes of palindromes starting with s
%o A083122     for i in range((len(s)+1)//2, len(s)+1):
%o A083122         for mid in [True, False]:
%o A083122             t = s[:i] + (s[:i-1][::-1] if mid else s[:i][::-1])
%o A083122             if t.startswith(s):
%o A083122                 yield t[len(s):]
%o A083122     yield from ("".join(p)+s[::-1] for p in pals("12"))
%o A083122 def agen():
%o A083122     s, seen = "1", {"1"}; yield 1
%o A083122     while True:
%o A083122         for t in folds(s):
%o A083122             if len(t) > 0 and set(t) != {"1"} and t not in seen: break
%o A083122         s = t; seen.add(t); yield int(t)
%o A083122 print(list(islice(agen(), 33))) # _Michael S. Branicky_, Aug 09 2022
%K A083122 base,nonn
%O A083122 1,2
%A A083122 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 23 2003
%E A083122 Corrected and extended by _Ray G. Opao_, Sep 22 2005
%E A083122 a(18) and beyond from _Michael S. Branicky_, Aug 09 2022