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A347336 Lexicographically earliest sequence of distinct positive integers such that the concatenation of a(n) and a(n+1) added to a(n+2) is a palindrome in base 10.

%I A347336 #15 Aug 30 2021 21:47:54
%S A347336 1,2,10,12,99,32,67,66,120,46,75,209,48,64,20,26,86,196,72,19,8,4,15,
%T A347336 9,22,7,5,13,42,319,105,808,793,1115,282,829,553,375,1080,493,308,
%U A347336 1186,617,194,522,1069,156,445,206,338,264,569,993,82,17,11,60,61,55,71,94,33,16,127,34,87
%N A347336 Lexicographically earliest sequence of distinct positive integers such that the concatenation of a(n) and a(n+1) added to a(n+2) is a palindrome in base 10.
%e A347336 [a(1), a(2)] + a(3) = [1, 2] + 10 = 12 + 10 = 22 (palindrome);
%e A347336 [a(2), a(3)] + a(4) = [2, 10] + 12 = 210 + 12 = 222 (palindrome);
%e A347336 [a(3), a(4)] + a(5) = [10, 12] + 99 = 1012 + 99 = 1111 (palindrome);
%e A347336 [a(4), a(5)] + a(6) = [12, 99] + 32 = 1299 + 32 = 1331 (palindrome); etc.
%o A347336 (Python)
%o A347336 def ispal(n): s = str(n); return s == s[::-1]
%o A347336 def aupton(terms):
%o A347336     alst, seen = [1, 2], {1, 2}
%o A347336     for n in range(2, terms):
%o A347336         an, partial_sum = 1, int(str(alst[-2]) + str(alst[-1]))
%o A347336         while an in seen or not ispal(partial_sum + an): an += 1
%o A347336         alst.append(an); seen.add(an)
%o A347336     return alst
%o A347336 print(aupton(66)) # _Michael S. Branicky_, Aug 28 2021
%Y A347336 Cf. A002113, A082216, A347335.
%K A347336 base,nonn
%O A347336 1,2
%A A347336 _Eric Angelini_ and _Carole Dubois_, Aug 28 2021