

A167161


The Catapult Sequence.


5



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, 36, 22, 38, 40, 41, 42, 44, 45, 47, 31, 35, 50, 52, 27, 55, 11, 58, 59, 61, 63, 64, 66, 67, 68, 70, 71, 49, 73, 54, 75, 76, 26, 79, 80, 82, 83, 85, 87, 51, 90, 53, 93, 95, 56, 98, 78
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OFFSET

0,3


COMMENTS

This sequence is conjectured to be a permutation of the nonnegative integers, generated by the following process:
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.
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 Xth term.


LINKS

Andrew Weimholt, Table of n, a(n) for n = 0..2000


EXAMPLE

Step 0: a(0)=0 catapults 1 a distance of 0 > 0,1,2,3,4,5,6,7,8.
Step 1: a(1)=1 catapults 2 a distance of 1 > 0,1,3,2,4,5,6,7,8.
Step 2: a(2)=3 catapults 2 a distance of 3 > 0,1,3,4,5,6,2,7,8.
Step 3: a(3)=4 catapults 5 a distance of 4 > 0,1,3,4,6,2,7,8,5.


PROG

(Sage)
def A167161(N): #Generates a(0)a(N)
A = range(3*N)
for n in range(N):
a = A.pop(n+1)
A.insert(n+A[n]+1, a)
return A[:N+1]
A167161(71) # Danny Rorabaugh, Mar 29 2015


CROSSREFS

Cf. A167162 the inverse permutation (conjectured).
Cf. A167163 number of times n is catapulted.
Cf. A167164 number which is catapulted by n.
Cf. A167165 total distance which n is catapulted.
Sequence in context: A225647 A135599 A283740 * A129000 A260158 A317093
Adjacent sequences: A167158 A167159 A167160 * A167162 A167163 A167164


KEYWORD

nonn


AUTHOR

Andrew Weimholt, Oct 29 2009


STATUS

approved



