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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 22:59 EST 2021. Contains 349426 sequences. (Running on oeis4.)