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%I #26 Aug 12 2022 09:18:05
%S 0,1,2,1,2,3,4,3,4,5,6,5,4,3,2,3,4,5,6,5,6,7,6,7,8,7,8,9,10,9,10,9,8,
%T 7,8,7,6,5,6,5,4,3,4,5,6,7,8,9,10,11,12,11,10,9,10,11,12,13,12,11,12,
%U 13,14,13,14,13,12,11,10,9,8,9,10,11,12,11,12,13
%N Position of the prime ant after n steps. If the value of the ant's position is prime, it steps to the right; if the value is composite, it divides by the least divisor, steps to the left, and adds the divisor.
%C a(n) gives the position after the n-th step on the infinite sequence (2, 3, 4, ...). If the value at the ant's position is prime, the ant steps to the right. If the value is composite, the ant divides the number by its least prime divisor, steps to the left, and adds the divisor to the new position.
%H Peter Kagey, <a href="/A293689/b293689.txt">Table of n, a(n) for n = 0..10000</a>
%H Code Golf Stack Exchange user Super Chafouin, <a href="https://codegolf.stackexchange.com/questions/144695/the-prime-ant">The Prime Ant</a>.
%e a(0) = 0:
%e 2 3 4 5 6 7 ...
%e ^ (prime; step to the right)
%e a(1) = 1:
%e 2 3 4 5 6 7 ...
%e ^ (prime; step to the right)
%e a(2) = 2:
%e 2 3 4 5 6 7 ...
%e ^ (composite; divide by 2, step to the left, add 2)
%e a(3) = 1:
%e 2 5 2 5 6 7 ...
%e ^ (prime; step to the right)
%e a(4) = 2:
%e 2 5 2 5 6 7 ...
%e ^
%t NestWhileList[If[PrimeQ[#2[[#1]] ], {#1 + 1, #2}, {#1 - 1, ReplacePart[#2, {#1 - 1 -> #2[[#1 - 1]] + #3, #1 -> #2[[#1]]/#3}]} & @@ {#1, #2, FactorInteger[#2[[#1]] ][[1, 1]]}] & @@ # &, {2, Range[10^2]}, First@ # < Length@ Last@ # &, 1, 78][[All, 1]] - 2 (* _Michael De Vlieger_, Oct 15 2017 *)
%K nonn,walk,look
%O 0,3
%A _Peter Kagey_, Oct 14 2017
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