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A329545 After a(1) = 1, add the even terms and subtract the odd ones, the result must always be a palindrome. This is the lexicographically earliest sequence of distinct positive integers with this property.

%I A329545 #31 Dec 11 2019 14:47:43
%S A329545 1,2,3,4,18,11,5,16,13,7,6,14,15,26,22,33,17,28,25,36,35,9,8,58,55,44,
%T A329545 46,10,20,30,73,77,66,24,40,50,103,79,68,34,23,81,48,47,80,83,72,54,
%U A329545 43,85,52,49,38,37,70,64,53,87,32,27,60,57,90,12,45,59,92,42,75,61,94,62,95,63,74,69,194
%N A329545 After a(1) = 1, add the even terms and subtract the odd ones, the result must always be a palindrome. This is the lexicographically earliest sequence of distinct positive integers with this property.
%C A329545 Negative palindromes are not allowed. After 50000 terms, the smallest unused integers are 964, 1020, 1029, 1031, 1038, 1041, 1047, 1051, ... and the largest used is 173410. The largest palindrome produced so far is 309903. Is the sequence a permutation of the integers > 0?
%C A329545 a(63411) = 964. _Rémy Sigrist_'s comment in A329544 shows that terms in A104444 are not in the sequence. Conjecture: Sequence is a permutation of positive integers not in A104444. - _Chai Wah Wu_, Dec 11 2019
%H A329545 Jean-Marc Falcoz, <a href="/A329545/b329545.txt">Table of n, a(n) for n = 1..49999</a>
%e A329545 The sequence starts with 1, smallest positive integer.
%e A329545 1 + 2 = 3 (palindrome)
%e A329545 1 + 2 - 3 = 0 (palindrome)
%e A329545 1 + 2 - 3 + 4 = 1 (palindrome)
%e A329545 1 + 2 - 3 + 4 + 18 = 22 (palindrome)
%e A329545 1 + 2 - 3 + 4 + 18 - 11 = 11 (palindrome)
%e A329545 1 + 2 - 3 + 4 + 18 - 11 - 5 = 6 (palindrome)
%e A329545 1 + 2 - 3 + 4 + 18 - 11 - 5 + 16 = 22 (palindrome), etc.
%o A329545 (PARI) A329545_vec(N, u=1, U, a, s=2, d)={vector(N, n, a=u; while(bittest(U, a-u)|| Vecrev(d=digits(s+(-1)^a*a))!=d|| (a>s&&bittest(a, 0)), a++); s+=(-1)^a*a; U+=1<<(a-u); while(bittest(U, 0), U>>=1; u++); a)} \\ _M. F. Hasler_, Nov 16 2019
%Y A329545 Cf. A329544 (same idea, but where the odd integers are added and the even ones are subtracted).
%Y A329545 Cf. A002113 (palindromes), A086862 (first differences of palindromes).
%Y A329545 Cf. A104444.
%K A329545 base,nonn
%O A329545 1,2
%A A329545 _Eric Angelini_ and _Jean-Marc Falcoz_, Nov 16 2019