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A227859 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. 1

%I

%S 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,

%T 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,

%U 3,5,6,7,4,8,9,5,1,6,1,7,0,0,8,2,9,3,2,4,5,3

%N 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.

%C 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).

%C 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.

%H E. Angelini, <a href="http://list.seqfan.eu/pipermail/seqfan/2013-November/011822.html">Skolem + digits (+ loop)</a>, SeqFan List, Nov 01 2013.

%e 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.

%e 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.

%o (PARI) a(n)=digits(8239243567489516170082932453674859161700121)[(n+17)%40+(n<6)*20+1]

%Y Cf. A227860.

%K nonn

%O 1,4

%A _Eric Angelini_ and _M. F. Hasler_, Nov 01 2013

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)