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A336740
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Lexicographically earliest sequence of distinct positive terms starting with a(1) = 110 such that the successive sums of the last two digits of the sequence reproduce, digit by digit, the sequence itself.
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1
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110, 19, 10, 9, 1, 8, 101, 7, 3, 89, 12, 6, 18, 4, 2, 99, 13, 11, 27, 36, 49, 29, 102, 5, 21, 15, 22, 45, 111, 54, 28, 211, 14, 311, 38, 23, 411, 511, 31, 32, 47, 69, 104, 611, 17, 711, 56, 59, 103, 65, 112, 26, 811, 121, 113, 74, 41, 83, 212, 58, 911, 122, 16, 24, 63, 37, 131, 33, 92, 98, 25, 129, 105, 42
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OFFSET
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1,1
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LINKS
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EXAMPLE
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After a(1) = 110 (the sum of the last two digits is 1) the smallest unused term allowing us to reconstruct the sequence by adding its last two digits is a(2) = 19 (1+9 = 10); the succession of the two sums so far is 1, 10;
a(3) = 10, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (1+0 = 1); the succession of the three sums so far is 1, 10, 1;
a(4) = 9, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (0+9 = 9); the succession of the four sums so far is 1, 10, 1, 9;
a(5) = 1, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (9+1 = 10); the succession of the five sums so far is 1, 10, 1, 9, 10 which is precisely the succession of the sequence's digits itself. Etc.
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CROSSREFS
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Cf. A336523 (product instead of sum).
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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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