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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 (list; graph; refs; listen; history; text; internal format)
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 X-th 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 A181590

Adjacent sequences:  A167158 A167159 A167160 * A167162 A167163 A167164

KEYWORD

nonn

AUTHOR

Andrew Weimholt, Oct 29 2009

STATUS

approved

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Last modified May 26 12:59 EDT 2017. Contains 287095 sequences.