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.

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

Offset

1,4

Comments

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.

Links

Table of n, a(n) for n=1..90.

E. Angelini, Skolem + digits (+ loop), SeqFan List, Nov 01 2013.

Example

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.

Prog

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

Crossrefs

Cf. A227860.

Sequence in context: A144241 A094173 A214370 * A026272 A193564 A022447

Adjacent sequences: A227856 A227857 A227858 * A227860 A227861 A227862

Keyword

nonn

Author

Eric Angelini and M. F. Hasler, Nov 01 2013

Status

approved