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A329545
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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.
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2
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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, 46, 10, 20, 30, 73, 77, 66, 24, 40, 50, 103, 79, 68, 34, 23, 81, 48, 47, 80, 83, 72, 54, 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
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OFFSET
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1,2
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COMMENTS
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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?
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LINKS
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EXAMPLE
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The sequence starts with 1, smallest positive integer.
1 + 2 = 3 (palindrome)
1 + 2 - 3 = 0 (palindrome)
1 + 2 - 3 + 4 = 1 (palindrome)
1 + 2 - 3 + 4 + 18 = 22 (palindrome)
1 + 2 - 3 + 4 + 18 - 11 = 11 (palindrome)
1 + 2 - 3 + 4 + 18 - 11 - 5 = 6 (palindrome)
1 + 2 - 3 + 4 + 18 - 11 - 5 + 16 = 22 (palindrome), etc.
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PROG
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(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
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CROSSREFS
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Cf. A329544 (same idea, but where the odd integers are added and the even ones are subtracted).
Cf. A002113 (palindromes), A086862 (first differences of palindromes).
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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