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A347335 Lexicographically earliest sequence of distinct nonnegative integers such that the sum of three consecutive terms is a palindrome in base 10.

%I A347335 #9 Aug 30 2021 21:47:24
%S A347335 0,1,2,3,4,15,14,26,37,25,39,13,36,6,24,47,17,35,49,27,12,5,16,23,38,
%T A347335 40,10,51,50,20,7,28,9,18,61,22,48,29,11,59,31,21,69,41,71,19,81,91,
%U A347335 30,60,101,111,70,122,80,90,32,100,110,42,120,130,53,8,141,63,58,121,33,68,131,43
%N A347335 Lexicographically earliest sequence of distinct nonnegative integers such that the sum of three consecutive terms is a palindrome in base 10.
%e A347335 a(1) + a(2) + a(3) = 0 + 1 + 2 = 3 (palindrome);
%e A347335 a(2) + a(3) + a(4) = 1 + 2 + 3 = 6 (palindrome);
%e A347335 a(3) + a(4) + a(5) = 2 + 3 + 4 = 9 (palindrome);
%e A347335 a(4) + a(5) + a(6) = 3 + 4 + 15 = 22 (palindrome); etc.
%o A347335 (Python)
%o A347335 def ispal(n): s = str(n); return s == s[::-1]
%o A347335 def aupton(terms):
%o A347335     alst, seen = [0, 1], {0, 1}
%o A347335     for n in range(2, terms):
%o A347335         an, partial_sum = 1, sum(alst[-2:])
%o A347335         while an in seen or not ispal(partial_sum + an): an += 1
%o A347335         alst.append(an); seen.add(an)
%o A347335     return alst
%o A347335 print(aupton(201)) # _Michael S. Branicky_, Aug 28 2021
%Y A347335 Cf. A228730.
%K A347335 base,nonn
%O A347335 1,3
%A A347335 _Eric Angelini_ and _Carole Dubois_, Aug 28 2021