A167161 The Catapult Sequence.

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

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 A317093

Adjacent sequences: A167158 A167159 A167160 * A167162 A167163 A167164

Keyword

nonn

Author

Andrew Weimholt, Oct 29 2009

Status

approved