A227860 Sequence of integers such that there are d terms between pairs of integers d. Cycle through d=0,1,2,3, trying to insert the least unused pair starting at the next free position.

0, 0, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3

Offset

1,4

Comments

After the two initial terms, the sequence enters the cycle (1,2,1,3,2,0,0,3) of length 8.

This is the lexicographically earliest (nontrivial) sequence of that type, with a range R={0,...,N}, following the example proposed by Eric Angelini (N=9: A227859), cf. link. Indeed, the ranges R={0,1} or R={0,1,2} are not possible. The range R={0,2} is also possible (cf. link).

Links

Table of n, a(n) for n=1..82.

M. F. Hasler, in reply to E. Angelini, Re: Skolem + digits + loop, SeqFan List, Nov 01 2013.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Formula

a(n) = a(n-8) for n>10. G.f.: -x^3*(3*x^7+2*x^4+3*x^3+x^2+2*x+1) / ((x-1)*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Nov 02 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.

Prog

(PARI) Vec((3*x^9+2*x^6+3*x^5+x^4+2*x^3+x^2)/(-x^8+1) + O(x^100)) \\ Colin Barker, Nov 02 2013

Crossrefs

Cf. A227859.

Sequence in context: A323730 A261250 A305354 * A020779 A260721 A275318

Adjacent sequences: A227857 A227858 A227859 * A227861 A227862 A227863

Keyword

nonn,easy

Author

M. F. Hasler, Nov 01 2013

Status

approved