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%I #14 Mar 08 2020 00:04:36
%S 0,1,3,4,6,7,5,10,2,13,12,14,16,18,19,21,23,8,25,15,28,17,24,32,33,20,
%T 36,22,38,40,41,42,44,45,47,31,35,50,52,27,55,11,58,59,61,63,64,66,67,
%U 68,70,71,49,73,54,75,76,26,79,80,82,83,85,87,51,90,53,93,95,56,98,78
%N The Catapult Sequence.
%C This sequence is conjectured to be a permutation of the nonnegative integers, generated by the following process:
%C Begin with the nonnegative integers in their normal positions. Starting with n=0, the number in position n, which will be our a(n), "catapults" the neighbor to its right a(n) spaces further to the right. Increment n and repeat.
%C Whether or not this is actually a permutation of the nonnegative integers depends on whether or not there exists a number that is catapulted an infinite number of times. If such a number (say X) exists, the inverse "permutation" will be undefined at the X-th term.
%H Andrew Weimholt, <a href="/A167161/b167161.txt">Table of n, a(n) for n = 0..2000</a>
%e Step 0: a(0)=0 catapults 1 a distance of 0 -> 0,1,2,3,4,5,6,7,8.
%e Step 1: a(1)=1 catapults 2 a distance of 1 -> 0,1,3,2,4,5,6,7,8.
%e Step 2: a(2)=3 catapults 2 a distance of 3 -> 0,1,3,4,5,6,2,7,8.
%e Step 3: a(3)=4 catapults 5 a distance of 4 -> 0,1,3,4,6,2,7,8,5.
%o (Sage)
%o def A167161(N): #Generates a(0)-a(N)
%o A = range(3*N)
%o for n in range(N):
%o a = A.pop(n+1)
%o A.insert(n+A[n]+1,a)
%o return A[:N+1]
%o A167161(71) # _Danny Rorabaugh_, Mar 29 2015
%Y Cf. A167162 the inverse permutation (conjectured).
%Y Cf. A167163 number of times n is catapulted.
%Y Cf. A167164 number which is catapulted by n.
%Y Cf. A167165 total distance which n is catapulted.
%K nonn
%O 0,3
%A _Andrew Weimholt_, Oct 29 2009
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