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A306804
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An irregular fractal sequence: underline a(n) iff the concatenation [a(n-1);a(n)] is divisible by a(n); all underlined terms rebuild the starting sequence.
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1
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1, 3, 1, 4, 6, 3, 1, 7, 8, 4, 9, 6, 3, 1, 11, 12, 13, 14, 7, 15, 16, 8, 4, 17, 18, 9, 6, 3, 1, 19, 21, 22, 11, 23, 24, 12, 26, 13, 27, 28, 14, 7, 29, 30, 15, 31, 32, 16, 8, 4, 33, 34, 17, 35, 36, 18, 9, 6, 3, 1, 37, 38, 19, 39, 40, 41, 42, 21, 43, 44, 22, 11, 45, 46, 23, 47, 48, 24, 12, 49, 51, 52, 26, 13, 53, 54, 27, 55, 56, 28, 14, 7
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OFFSET
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1,2
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COMMENTS
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The sequence S starts with a(1) = 1 and a(2) = 3. S is extended by duplicating the first term A among the not yet duplicated terms, under the condition that the concatenation [last term Z of the sequence;A] is divisible by A. If this is not the case, we then extend S with the smallest integer X not yet present in S such that the concatenation [last term Z of the sequence;X] is not divisible by X. This is the lexicographically first sequence with this property. The terms 2 and 5 will never appear.
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LINKS
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EXAMPLE
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S starts with a(1) = 1 and a(2) = 3
Can we duplicate a(1) to form a(3)? Yes, as [31] is divisible by 1, of course; thus a(3) = 1.
Can we duplicate a(2) to form a(4)? No, as [13] is not divisible by 3; we thus extend S with the smallest integer X not yet in S such that [a(3);X] is not divisible by X. We get X = 4 and thus a(4) = 4.
Can we duplicate a(2) to form a(5)? No, as [43] is not divisible by 3; we thus extend S with the smallest integer X not yet in S such that [a(4);X] is not divisible by X. We get X = 6 and thus a(5) = 6.
Can we duplicate a(2) to form a(6)? Yes, as [63] is divisible by 3, of course; thus a(6) = 3.
Can we duplicate a(3) to form a(7)? Yes, as [31] is divisible by 1, of course; thus a(7) = 1.
Can we duplicate a(4) to form a(8)? No, as [14] is not divisible by 4; we thus extend S with the smallest integer X not yet in S such that [a(7);X] is not divisible by X. We get X = 7 and thus a(8) = 7.
Can we duplicate a(4) to form a(9)? No, as [74] is not divisible by 4; we thus extend S with the smallest integer X not yet in S such that [a(8);X] is not divisible by X. We get X = 8 and thus a(9) = 8.
Can we duplicate a(4) to form a(10)? Yes, as [84] is divisible by 4, of course; thus a(10) = 4.
Etc.
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CROSSREFS
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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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