# [seqfan] Re: a permutation of the naturals

Andrew Weimholt andrew.weimholt at gmail.com
Thu Oct 29 10:58:24 CET 2009

```The Catapult Sequence will be A167161
The four related sequences will be A167162 through A167165.
I sent a separate email with b-files attached, but I got an automated
reply indicating that
the message won't post to the SeqFan list until moderator approval due
to exceeding the 40kb limit.

Here are the submission lines again...

%I A167161
%S A167161 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 A167161 36,22,38,40,41,42,44,45,47,31,35,50,52,27,55,11,58,59,61,63,64,66,67,
%U A167161 68,70,71,49,73,54,75,76,26,79,80,82,83,85,87,51,90,53,93,95,56,98,78
%N A167161 The Catapult Sequence
%C A167161 This sequence is conjectured to be a permutation of the non-negative
%C A167161 integers, generated by the following process:
%C A167161 Begin with the non-negative integers in their normal positions.
%C A167161 Starting with n=0, the number in position n, which will be our a(n),
%C A167161 "catapults" the neighbor to its right a(n) spaces further to the
%C A167161 right. Increment n and repeat.
%C A167161 Whether or not this is actually a permutation of the non-negative
%C A167161 integers depends on whether or not there exists a number that is
%C A167161 catapulted an infinite number of times. If such a number (say X)
%C A167161 exists, the inverse "permutation" will be undefined at the Xth term.
%H A167161 Andrew Weimholt, <a href="b167161.txt">Table of n, a(n) for
n = 0..2000</a>
%e A167161 step 0: a(0)=0 catapults 1 a distance of 0 -> 0,1,2,3,4,5,6,7,8
%e A167161 step 1: a(1)=1 catapults 2 a distance of 1 -> 0,1,3,2,4,5,6,7,8
%e A167161 step 2: a(2)=3 catapults 2 a distance of 3 -> 0,1,3,4,5,6,2,7,8
%e A167161 step 3: a(3)=4 catapults 5 a distance of 4 -> 0,1,3,4,6,2,7,8,5
%Y A167161 Cf. A167162 the inverse permutation (conjectured).
%Y A167161 Cf. A167163 number of times n is catapulted.
%Y A167161 Cf. A167164 number which is catapulted by n.
%Y A167161 Cf. A167165 total distance which n is catapulted.
%K A167161 nonn
%O A167161 0,3
%A A167161 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A167162
%S A167162 0,1,8,2,3,6,4,5,17,152,7,41,10,9,11,19,12,21,13,14,25,15,27,16,22,18,
%T A167162 57,39,20,159537,78,35,23,24,218,36,26,94,28,84,29,30,31,112,32,33,525,
%U A167162 34,104,52,37,64,38,66,54,40,69,82,42,43,74,44,76,45,46,80,47,48,49,443
%N A167162 Inverse Permutation (conjectured) of Catapult Sequence (A167161).
%C A167162 Whether or not this sequence is defined for all n depends on whether
%C A167162 or not A167161 is a true permutation of the non-negative integers
%C A167162 (see comments under A167161).
%H A167162 Andrew Weimholt, <a href="b167162.txt">Table of n, a(n) for
n = 0..2000</a>
%e A167162 a(2) = 8 because A167161(8) = 2.
%Y A167162 Cf. A167161 The Catapult Sequence.
%Y A167162 Cf. A167163 number of times n is catapulted in generation of A167161.
%Y A167162 Cf. A167164 number catapulted by n in generation of A167161.
%Y A167162 Cf. A167165 total distance which n is catapulted in
generation of A167161.
%K A167162 nonn
%O A167162 0,3
%A A167162 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A167163
%S A167163 0,1,3,0,0,1,0,0,2,6,0,3,1,0,0,1,0,1,0,0,1,0,1,0,1,0,2,2,0,17,3,1,0,0,4,
%T A167163 1,0,3,0,2,0,0,0,3,0,0,5,0,2,1,0,1,0,1,1,0,1,2,0,0,1,0,1,0,0,1,0,0,0,4,
%U A167163 0,0,1,0,1,0,0,1,1,0,0,1,0,0,5,0,5,0,1,2,0,1,3,0,1,0,1,2,0,1
%N A167163 Number of times n is "catapulted" in generation of the
Catapult Sequence (A167161).
%H A167163 Andrew Weimholt, <a href="b167163.txt">Table of n, a(n) for
n = 1..2000</a>
%e A167163 a(2) = 3, because in generating A167161, the number 2 is catapulted
%e A167163 3 times (first by 1, then by 3, and finally by 6).
%Y A167163 Cf. A167161 The Catapult Sequence.
%Y A167163 Cf. A167162 The inverse permutation (conjectured) of A167161.
%Y A167163 Cf. A167164 number catapulted by n in generation of A167161.
%Y A167163 Cf. A167165 total distance which n is catapulted in
generation of A167161.
%K A167163 nonn
%O A167163 0,3
%A A167163 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A167164
%S A167164 1,2,12,2,5,9,2,8,24,210,11,57,8,9,15,27,17,30,11,20,35,22,27,9,31,26,
%T A167164 78,54,29,219348,37,49,11,34,303,29,37,130,39,117,9,30,43,153,26,46,719,
%U A167164 48,117,30,51,89,53,92,43,56,97,43,34,60,104,62,107,37,65,112,57,39
%N A167164 The number which is "catapulted" by n in the generation of
the Catapult Sequence (A167161).
%C A167164 Whether or not this sequence is defined for all n depends on whether
%C A167164 or not A167161 is a true permutation of the non-negative integers
%C A167164 (see comments under A167161).
%H A167164 Andrew Weimholt, <a href="b167164.txt">Table of n, a(n) for
n = 1..2000</a>
%e A167164 a(2) = 12, because in the generation of the A167161,
%e A167164 2 eventually catapults 12.
%Y A167164 Cf. A167161 The Catapult Sequence.
%Y A167164 Cf. A167162 The inverse permutation (conjectured) of A167161.
%Y A167164 Cf. A167163 number of times n is catapulted in generation of A167161.
%Y A167164 Cf. A167165 total distance which n is catapulted in
generation of A167161.
%Y A167164
%K A167164 nonn
%O A167164 0,2
%A A167164 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

%I A167165
%S A167165 0,0,10,0,0,4,0,0,19,272,0,60,2,0,0,14,0,16,0,0,19,0,21,0,8,0,69,37,0,
%T A167165 302158,107,24,0,0,366,20,0,129,0,105,0,0,0,153,0,0,917,0,129,31,0,50,0,
%U A167165 52,27,0,55,77,0,0,59,0,61,0,0,64,0,0,0,743,0,0,71,0,73,0,0,76,26,0,0
%N A167165 Total distance which n is "catapulted" in the generation of
the Catapult Sequence (A167161).
%C A167165 Whether or not this sequence is defined for all n depends on whether
%C A167165 or not A167161 is a true permutation of the non-negative integers
%C A167165 (see comments under A167161).
%H A167165 Andrew Weimholt, <a href="b167165.txt">Table of n, a(n) for
n = 1..2000</a>
%e A167165 a(2) = 10, because 2 is catapulted by 1, 3, and 6 for a total
%e A167165 distance of 1+3+6 = 10
%Y A167165 Cf. A167161 The Catapult Sequence.
%Y A167165 Cf. A167162 The inverse permutation (conjectured) of A167161.
%Y A167165 Cf. A167163 number of times n is catapulted in generation of A167161.
%Y A167165 Cf. A167164 number catapulted by n in generation of A167161.
%Y A167165
%K A167165 nonn
%O A167165 0,3
%A A167165 Andrew Weimholt (andrew(AT)weimholt.com), Oct 29 2009

Andrew

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