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A227859
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Sequence of integers such that there are d terms between pairs of integers d. Cycle through d=0,...,9, trying to insert the least unused pair starting at the next free position.
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1
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0, 0, 1, 2, 1, 3, 2, 4, 5, 3, 6, 7, 4, 8, 5, 9, 1, 6, 1, 7, 0, 0, 8, 2, 3, 9, 2, 4, 3, 5, 6, 7, 4, 8, 9, 5, 1, 6, 1, 7, 0, 0, 8, 2, 9, 3, 2, 4, 5, 3, 6, 7, 4, 8, 5, 9, 1, 6, 1, 7, 0, 0, 8, 2, 3, 9, 2, 4, 3, 5, 6, 7, 4, 8, 9, 5, 1, 6, 1, 7, 0, 0, 8, 2, 9, 3, 2, 4, 5, 3
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OFFSET
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1,4
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COMMENTS
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After the first 5 initial terms, there starts a cycle of 2x20 terms, (3,2,4,...,9,2,4,...), the two half-cycles differing only in 3 transpositions (3,9), (5,3) and (5,9).
The sequence is not related to the base-10 (or any other) representation of the numbers. The choice of the range {0,...,9} is somewhat arbitrary, the same could be done for other ranges. But one can see that R={0,1} and R={0,1,2} are not possible, while R={0,2} or R={0,1,2,3} for example are possible, see A227860.
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LINKS
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EXAMPLE
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Between a(1)=0 and a(2)=0 there are 0 other terms. Then one can place a(3)=1 and has to set a(5)=1 as to have 1 term in between these two. Then one can set a(4)=2=a(7). Then the next free position is a(6)=3=a(10), etc.
After setting a(16)=9=a(26), one cannot place the pair (0,0) starting with the next free position a(17), because a(18)=6 is already set. So the pair a(17)=1=a(19) is inserted, and only thereafter the pair (0,0) at a(21)=0=a(22), then another pair (2,2), and so on.
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PROG
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(PARI) a(n)=digits(8239243567489516170082932453674859161700121)[(n+17)%40+(n<6)*20+1]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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